Chapter 9 Testbank (1)

CHAPTER 9—HYPOTHESIS TESTS MULTIPLE CHOICE

1. The The sum sum of the the valu values es of α and β a. alwa always ys add add up up to 1.0 1.0 b. always add up to 0.5 c. is the probab probabil ility ity of Type Type II erro error r alternatives is correct. d. None of these alternatives ANS: 

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T"!: #ypothesis Tests

$. %hat type of error error occurs occurs if you you fail fail to re&ect re&ect # 0 when' in fact' it is not true( a. Type II b. Type I c. either either Type Type I or Type Type II' depend dependin) in) on the level level of of si)nifica si)nificance nce d. either either Type Type I or Type II' II' dependin) dependin) on on whether whether the the test is one tail tail or two tail tail ANS: A

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*. An assumpt assumption ion made made about about the value value of a populat population ion paramete parameterr is called called a a. hypothesis b. conclusion c. confidence d. si)n i)nifi ificanc cancee ANS: A

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+. The probabi probability lity of committ committin) in) a Type Type I error when when the null null hypothesi hypothesiss is true is a. the the con confi fide denc ncee lev level el b. β c. )reater th than 1 d. the the ,ev ,evel el of Si) Si)ni nifi fica canc ncee ANS: 

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5. In hyp hypot othe hesi siss test testin in)' )' a. the smalle smallerr the Type Type I error' error' the the smaller smaller the Type Type II error error will will be b. the smaller the Type I error' error' the lar)er the Type II error will be c. Type Type II error error will will not not be effe effecte cted d by Type Type I error error d. the sum sum of Type I and Ttype Ttype II errors errors must e-ual e-ual to 1 ANS: 

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/. In hypothesis hypothesis testin testin)' )' the tentative tentative assumpti assumption on about about the populatio population n parameter parameter is a. the the alte altern rnat ativ ivee hypo hypoth thes esis is b. the null hypothesis hypothesis c. either either the null null or the altern alternati ative ve alternatives is correct. d. None of these alternatives ANS: 

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. or or a lowe lowerr tail tail tes test' t' the the p2value is the probability of obtainin) a value for the test statistic a. at least least as as small small as that that prov provide ided d by the the sampl samplee

b. at least as lar)e as that provided provided by the sample sample c. at least least as small small as that that provided provided by the the popula population tion d. at least least as lar)e lar)e as that that provid provided ed by the popul populatio ation. n. ANS: A

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3. The p2value is a probability that measures the support 4or lac of support6 for the a. null ull hy hypoth pothes esis is b. alternative hypothesis hypothesis c. either either the the null null or the the altern alternati ative ve hypot hypothes hesis is d. samp sample le stat statis isti ticc ANS: A

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7. The p2value a. is the the same same as as the the 8 sta stati tist stic ic b. measures the number of standard standard deviations from the the mean c. is a distance d. is a prob probab abil ilit ity y ANS: 

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10. 10. or or a two2 two2ta tail il tes test' t' the the p2value is the probability of obtainin) a value for the test statistic as a. liely liely as that that provi provided ded by the the samp sample le b. unliely as that provided provided by the sample c. liely liely as as that that provi provided ded by by the the popul populati ation on d. unlie unliely ly as that that provi provided ded by by the popu populat lation ion ANS: 

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11. In hypothes hypothesis is testin) testin) if if the null null hypothesi hypothesiss is re&ected re&ected'' a. no conc conclus lusion ionss can can be draw drawn n from from the the test test b. the alternative hypothesis hypothesis is true c. the data data must must have have been been accum accumula ulated ted inco incorre rrectl ctly y d. the sample sample si9e si9e has has b been een too small small ANS: 

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1$. 1$. The level level of of si)nif si)nifica icance nce is the the a. maimu maimum m allowa allowable ble prob probabi abilit lity y of Type Type II error error b. maimum allowable probability probability of Type I error error c. same same as the the confi confiden dence ce coef coeffic ficien ientt d. same as the p2value ANS: 

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1*. The power curve provides provides the probabili probability ty of of a. correc correctly tly acce accepti ptin) n) the the null null hypot hypothes hesis is b. incorrectly acceptin) acceptin) the null hypothesis hypothesis c. correctly correctly re&ectin) re&ectin) the alternati alternative ve hypothes hypothesis is d. correc correctly tly re&e re&ecti ctin) n) the the null null hypoth hypothesi esiss ANS: 

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1+. 1+. A Type Type II II error error is comm committ itted ed when when a. a true true alterna alternative tive hypothes hypothesis is is is mista mistaenly enly re&ected re&ected

b. a true null hypothesis hypothesis is mistaenly re&ected re&ected c. the sample sample si9e si9e has has b been een too small small d. not enou enou)h )h infor informat mation ion has has been been avail availab able le ANS: A

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15. The error error of of re&ectin re&ectin) ) a true true null null hypoth hypothesis esis is a. a Type I error b. a Type II error c. is the same as β d. committed committed when not enou)h enou)h inform informatio ation n is available available ANS: A

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1/. The level level of si)nifica si)nificance nce in hypothes hypothesis is testin) testin) is the the probabilit probability y of a. accep acceptin tin) ) a true true nul nulll hypo hypothe thesis sis b. acceptin) a false null null hypothesis c. re&ect re&ectin) in) a true true null null hyp hypoth othesi esiss alternatives is correct. d. None of these alternatives ANS: ;

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1. 1. The level level of si)nif si)nifica icance nce a. can can be be any any posi positi tive ve valu valuee b. can be any value c. is 41 2 con confi fide denc ncee lev level el66 d. can be any any valu valuee betwe between en 21.7 21.7/ / to 1.7/ 1.7/ ANS: ;

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13. In hypothesis hypothesis testin) if the null hypothesis hypothesis has been re&ected when the alternative hypothesis hypothesis has has been true' a. a Type Type I err error or has has bee been n commi committ tted ed b. a Type II error has been committed committed c. either either a Type Type I or or Type Type II error error has has been been commi committe tted d d. the correc correctt decis decision ion has been been made made ANS: 

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17. The probab probabilit ility y of main) main) a Type Type I error error is denoted denoted by a. α b. β c. 1 2 α d. 1 2 β ANS: A

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$0. The probab probabilit ility y of main) main) a Type Type II error is is denoted denoted by a. α b. β c. 1 2 α d. 1 2 β ANS: 

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$1. %hen the the followin) followin) hypoth hypotheses eses are bein) bein) tested tested at a level level of si)nifica si)nificance nce of α #0: µ 500 #a: µ < 500 the null hypothesis will be re&ected if the p2value is a. α b. = α c. = α>$ d. 1 2 α>$ ANS: A

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$$. %hen the p2value is used for hypothesis testin)' the null hypothesis is re&ected if a. p2value α b. α < p2value c. p2value α d. p2value ? 1 2 α ANS: A

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$*. In order order to test the follo followin) win) hypothese hypothesess at an α level of si)nificance #0: µ 300 #a: µ = 300 the null hypothesis will be re&ected if the test statistic 8 is a. 8α b. < 8α c. < 28α d. ? α ANS: A

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$+. $+. %hich %hich of the the foll followi owin) n) does does not need to be nown in order to compute the p2value( a. nowled)e nowled)e of whether whether the test test is is one2tail one2tailed ed or or two2tai two2tailed led b. the value of the test statistic statistic c. the the lev level el of of si) si)ni nifi fica canc ncee alternatives is correct. d. None of these alternatives ANS: ;

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$5. $5. In the hypo hypothe thesis sis test testin) in) proc procedu edure' re' α is a. the the lev level el of of si) si)ni nifi fica canc ncee b. the critical value c. the the con confi fide denc ncee lev level el d. 1 2 leve levell of of si) si)ni nifi fica canc ncee ANS: A

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$/. If a hypothes hypothesis is test test leads to to the re&ectio re&ection n of the null null hypothe hypothesis' sis' a. a Type Type II II error error mus mustt have have been been commit committed ted b. a Type II error may have been committed committed

c. a Type Type I error error must must have have been been comm committ itted ed d. a Type Type I error error may may have have been been commi committe tted d ANS:  $. As a. b. c. d.

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the the test test statistic statistic becomes becomes lar)er' lar)er' the p2value )ets smaller becomes lar)er stays stays the same' since since the sample sample si9e si9e has not been been chan)ed chan)ed beco become mess ne)a ne)ati tive ve

ANS: A

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$3. The p2value ran)es between a. 9ero 9ero and and in infin finity b. minus infinity to to plus infinity c. 9ero to one d. 21 to @1 ANS: ;

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$7. or a lower lower bounds bounds one2tailed one2tailed test' test' the test test statis statistic tic z is is determined determined to be 9ero. The p2value for this test is a. 9ero b. 20.5 c. @0.5 d. 1.00 ANS: ;

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*0. In a two2tailed hypothesis test situation' the test test statistic is determined to be t ? 2$./7$. The sample si9e has been +5. +5. The p2value for this test is a. 20.005 b. @0.005 c. 20.01 d. @0.01 ANS: 

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*1. In a lower lower one2ta one2tail il hypothes hypothesis is test test situatio situation' n' the p2value is determined determined to be 0.$. 0.$. If the sample si9e si9e for this test is 51' the t statistic statistic has a value of a. 0.3+7 b. 20.3+7 c. 1.$77 d. 21.$77 ANS: 

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*$. If a hypothes hypothesis is is re&ected re&ected at at the 5 level level of of si)nifican si)nificance' ce' it a. will will alway alwayss be re&ect re&ected ed at at the the 1 level level b. will always be accepted accepted at the 1 level c. will will neve neverr be tested tested at the 1 level level d. may be be re&ect re&ected ed or not not re&ec re&ected ted at at the the 1 level level ANS: 

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**. If a hypothes hypothesis is is not not re&ected re&ected at the the 5 level level of si)nifi si)nificance cance'' it a. will will also also not not be be re&ect re&ected ed at the 1 leve levell b. will always be re&ected re&ected at the 1 level c. will will somet sometime imess be re&e re&ecte cted d at the the 1 1 level level alternatives is correct. d. None of these alternatives ANS: A

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*+. *+. If the the probab probabili ility ty of of a Type Type I erro errorr 4 α6 is 0.05' then the probability of a Type II error 4 β6 must be a. 0.05 b. 0.75 c. 0.0$5 alternatives is correct. d. None of these alternatives ANS: 

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*5. If the level level of si)nificance si)nificance of a hypothesis hypothesis test is raised from .01 to .05' the probability probability of of a Type II error a. will will also also increa increase se from from .01 .01 to to .05 .05 b. will not chan)e c. will de decrease d. will ill incr increa easse ANS: ;

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*/. If a hypot hypothesi hesiss is re&ect re&ected ed at 75 confi confidence dence'' it a. will will alway alwayss be acce accepte pted d at 70 70 conf confide idence nce b. will always be re&ected re&ected at 70 confidence c. will will somet sometime imess be re&ec re&ected ted at at 70 conf confide idence nce alternatives is correct. d. None of these alternatives ANS: 

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*. or a two2tailed two2tailed test at 3/.1$ 3/.1$ confid confidence' ence' 8 ? a. 1.7/ b. 1.+3 c. 1.07 d. 0.3/ ANS: 

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*3. or a one2tai one2tailed led test test 4lower 4lower tail6 tail6 at at 7*. 7*. confiden confidence' ce' 8 ? a. 21.3/ b. 21.5* c. 21.7/ d. 21./+5 ANS: 

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*7. Bead the 8 statistic from from the normal normal distribution distribution table and circle the correct answer. A one2tailed test test 4upper tail6 at 3. confidenceC 8 ? a. 1.5+ b. 1.7/ c. 1./+5 d. 1.1/

ANS: 

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+0. or a two2tai two2tailed led test' test' a sample sample of $0 at at 30 confid confidence' ence' t ? a. 1.*$3 b. $.5*7 c. 1.*$5 d. $.5$3 ANS: A

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+1. or a one2tail one2tailed ed test 4upper 4upper tail6 tail6'' a sample si9e si9e of 13 at at 75 confide confidence' nce' t ? a. $.1$ b. 2$.1$ c. 21.+0 d. 1.+0 ANS: 

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+$. or a one2tail one2tailed ed test 4lower 4lower tail6 tail6'' a sample si9e si9e of 10 at 70 confid confidence' ence' t ? a. 1.*3* b. $.3$1 c. 21.*3* d. 2$.3$1 ANS: ;

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+*. A two2tail two2tailed ed test test is perfor performed med at 75 75 confiden confidence. ce. The The p2value is determined to be 0.07. The null hypothesis a. mu musst be be re& re&ec ecte ted d b. should not be re&ected re&ected c. could could be re&e re&ecte cted' d' depend dependin) in) on on the sampl samplee si9e si9e d. has been been desi desi)ne )ned d inco incorre rrectl ctly y ANS: 

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++. or a two2tailed two2tailed test at 73.+ 73.+ confid confidence' ence' 8 ? a. 1.7/ b. 1.1+ c. $.+1 d. 0.3/1$ ANS: ;

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+5. or a one2tai one2tailed led test test 4lower 4lower tail6 tail6 at at 37.3 37.3 confiden confidence' ce' 8 ? a. 21.$ b. 21.5* c. 21.7/ d. 21./+ ANS: A

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+/. or a one2tai one2tailed led test test 4upper 4upper tail6 tail6 at at 7*. 7*. confiden confidence' ce' 8 ? a. 1.50 b. 1.7/ c. 1./+5 d. 1.5*

ANS: 

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+. or a one2tail one2tailed ed test 4upper 4upper tail6 tail6'' a sample si9e si9e of $/ at at 70 confide confidence' nce' t ? a. 1.*1/ b. 21.*1/ c. 21.+0 d. 1.+0 ANS: A

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+3. or a one2tailed one2tailed test test 4lower 4lower tail6 with with $$ de)rees de)rees of freedom freedom at 75 75 confidence' confidence' the the value of t ? a. 21.*3* b. 1.*3* c. 21.1 d. 21.$1 ANS: ;

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+7. or a one2tailed one2tailed hypothes hypothesis is test test 4upper 4upper tail6 tail6 the p2value is computed to be 0.0*+. If the test is bein) conducted at 75 confidence' the null hypothesis a. could could be re&ecte re&ected d or not not re&ected re&ected depend dependin) in) on the sample sample si9e si9e b. could be re&ected or not not re&ected dependin) on the value of the mean of the sample sample c. is not re&e re&ect cted ed d. is re&ected ANS: 

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50. In a two2tailed two2tailed hypot hypothesi hesiss test the test test statisti statisticc is determined determined to be be 8 ? 2$.5. The p2value for this test is a. 21.$5 b. 0.+7*3 c. 0.00/$ d. 0.01$+ ANS: 

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51. In a one2tailed one2tailed hypothe hypothesis sis test 4lower 4lower tail6 tail6 the test statisti statisticc is determined determined to be 2$. The p2value for this test is a. 0.+$ b. 0.0$$3 c. 0.005/ d. 0.5$$3 ANS: 

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5$. The avera)e avera)e manufacturin) manufacturin) wor wee wee in metropolitan ;hattanoo)a was +0.1 +0.1 hours hours last year. It is believed that the recession recession has led to a reduction reduction in the avera)e wor wee. wee. To test the validity validity of this belief' the hypotheses are a. #0: µ < +0.1 #a: µ ≥ +0.1 b. #0: µ ≥ +0.1 #a: µ < +0.1 c. #0: µ > +0.1 #a: µ ≤ +0.1 d. #0: µ = +0.1 #a: µ ≠ +0.1 ANS: 

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5*. The avera)e avera)e monthly monthly rent for one2bedroom one2bedroom apartments apartments in ;hattanoo)a ;hattanoo)a has been D00. ecause of of the downturn in the real estate maret' it is believed that there has been a decrease in the avera)e rental. The correct hypotheses to be tested are a. #0: µ ≥ 00 #a: µ < 00 b. #0: µ ? 00 #a: µ ≠ 00 c. #0: µ > 00 #a: µ ≤00 d. #0: µ < 00 #a: µ ≥ 00 ANS: A

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5+. A machine machine is desi)ned to fill fill toothpaste toothpaste tubes with 5.3 ounces ounces of toothpaste. The manufacturer manufacturer does does not want any underfillin) or overfillin). overfillin). The correct hypotheses to be tested are a. #0: µ ≠ 5.3 #a: µ ? 5.3 b. #0: µ ? 5.3 #a: µ ≠ 5.3 c. #0: µ > 5.3 #a: µ ≤ 5.3 d. #0: µ ≥ 5.3 #a: µ < 5.3 ANS: 

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55. The avera)e avera)e hourly hourly wa)e of computer computer pro)rammer pro)rammerss with $ years of eperien eperience ce has been D$1.30. D$1.30. ecause of hi)h demand for computer computer pro)rammers' it is believed there has has been a si)nificant increase in the avera)e wa)e wa)e of computer pro)rammers. To test whether or not not there has been an increase' the correct hypotheses to be tested are a. #0: µ < $1.30 #a: µ ≥ $1.30 b. #0: µ ? $1.30 #a: µ ≠ $1.30 c. #0: µ > $1.30 #a: µ ≤ $1.30 d. #0: µ ≤ $1.30 #a: µ = $1.30 ANS: 

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5/. A student believes that that the avera)e avera)e )rade on on the final final eamination in statistics statistics is at least 35. She plans on tain) a sample to test her belief. The correct set of hypotheses is a. #0: µ < 35 #a: µ 35 b. #0: µ 35 #a: µ = 35 c. #0: µ 35 #a: µ < 35 d. #0: µ = 35 #a: µ 35 ANS: ;

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5. In the past' past' 5 of of the tourists tourists who visited ;hattanoo)a ;hattanoo)a went went to see Boc ;ity. The mana)ement of Boc ;ity recently undertoo an etensive promotional campai)n. They are interested in determinin) whether the promotional campai)n actually increased the proportion of tourists visitin) Boc ;ity. The correct set of hypotheses is a. #0: ! = 0.5 #a: ! 0.5 b. #0: ! < 0.5 #a: ! 0.5 c. #0: ! 0.5 #a: ! < 0.5 d. #0: ! 0.5 #a: ! = 0.5 ANS: 

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53. The avera)e avera)e life epectan epectancy cy of tires produced produced by the %hitney %hitney Tire Tire ;ompany ;ompany has been +0'000 +0'000 miles. miles. Eana)ement believes that due to a new production process' the life epectancy of their tires has increased. In order to test the validity of their belief' the correct set of hypotheses is

a. b. c. d.

#0: µ < +0'000 #0: µ +0'000 #0: µ = +0'000 #0: µ +0'000

ANS: 

#a: µ +0'000 #a: µ = +0'000 #a: µ +0'000 #a: µ < +0'000 !TS: 1


57. A soft drin drin fillin) machine' when in perfect ad&ustment' fills fills the bottles with with 1$ ounces ounces of soft soft drin. Any over fillin) or under fillin) results in the shutdown and read&ustment of the machine. To determine whether or not the machine is properly ad&usted' the correct set of hypotheses is a. #0: µ < 1$ #a: µ 1$ b. #0: µ 1$ #a: µ = 1$ c. #0: µ ≠ 1$ #a: µ ? 1$ d. #0: µ ? 1$ #a: µ ≠ 1$ ANS: 

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/0. The academic planner of a university thins that that at least least *5 of the entire entire student body attends attends summer school. The correct set of hypotheses to test his belief is a. #0: ! = 0.*5 #a: ! 0.*5 b. #0: ! 0.*5 #a: ! = 0.*5 c. #0: ! 0.*5 #a: ! < 0.*5 d. #0: ! = 0.*5 #a: ! 0.*5 ANS: ;

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/1. The mana)er of an automobile automobile dealership dealership is considerin) a new bonus bonus plan in in order to increase sales. sales. ;urrently' the mean sales rate per salesperson is five automobiles per month. The correct set of hypotheses for testin) the effect of the bonus plan is a. #0: µ < 5 #a: µ 5 b. #0: µ 5 #a: µ = 5 c. #0: µ = 5 #a: µ 5 d. #0: µ 5 #a: µ < 5 ANS: 

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/$. Four investment investment eecutive claims that the avera)e yearly rate of return on the stocs stocs she recommends is at least 10.0. Fou plan on tain) a sample to test her claim. The correct set of hypotheses is a. #0: µ < 10.0 #a: µ 10.0 b. #0: µ 10.0 #a: µ = 10.0 c. #0: µ = 10.0 #a: µ 10.0 d. #0: µ 10.0 #a: µ < 10.0 ANS: 

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/*. A weatherman stated that the avera)e temperature durin) durin) Guly in ;hattanoo)a ;hattanoo)a is 30 30 de)rees or less. A sample of *$ Gulys is taen. The correct set of hypotheses is a. #0: µ 30 #a: µ < 30 b. #0: µ 30 #a: µ = 30 c. #0: µ ≠ 30 #a: µ ? 30 d. #0: µ < 30 #a: µ = 30 ANS: 

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/+. The schoolHs schoolHs newspaper reported that the proportion proportion of students students ma&orin) ma&orin) in business business is at least *0. Fou plan on tain) a sample to test the newspaperHs claim. The correct set of hypotheses is a. #0: ! < 0.*0 #a: ! 0.*0 b. #0: ! 0.*0 #a: ! = 0.*0 c. #0: ! 0.*0 #a: ! < 0.*0 d. #0: ! = 0.*0 #a: ! 0.*0 ANS: ;

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NABBJIN: hibit hibit 07201 Exhibit 9! n ? */

? $+./

S ? 1$

#0: µ $0 #a: µ = $0

NABBN /5. Befer to hibi hibitt 721. 721. The The test test statis statistic tic is is a. $.* b. 0.*3 c. 2$.* d. 20.*3 ANS: A

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//. //. Befer Befer to hibi hibitt 721. 721. The p2value is between a. 0.00 .005 to 0.01 b. 0.01 to 0.0$5 c. 0.0$ .0$5 to 0.05 d. 0.05 .05 to 0.10 .10 ANS: 

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/. Befer to hibit hibit 721. 721. If the test is done at 75 75 confidence' confidence' the null null hypothesi hypothesiss should should a. not be re&e re&ect cted ed b. be re&ected c. Not enou) enou)h h informa information tion is )iven )iven to to answer answer this this -uestion -uestion.. alternatives is correct. d. None of these alternatives ANS: 

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NABBJIN: hibit hibit 0720$ Exhibit 9" n ? /+

? 50

s ? 1/

NABBN /3. Befer to hibi hibitt 72$. 72$. The test statistic statistic e-uals e-uals a. 2+ b. 2* c. 2$

#0: µ 5+ #a: µ < 5+

d. 21 ANS: ;

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/7. /7. Befer Befer to hibi hibitt 72$. 72$. The p2value is between a. .005 to to .0 .01 b. .01 to .0$5 c. .0$5 to to .0 .05 d. .05 to .01 ANS: 

!TS: 1


0. Befer to hibit hibit 72$. 72$. If the test is done at 75 75 confidence' confidence' the null null hypothesi hypothesiss should should a. not be re&e re&ect cted ed b. be re&ected c. Not enou) enou)h h informa information tion is )iven )iven to to answer answer this this -uestion -uestion.. alternatives is correct. d. None of these alternatives ANS: 

!TS: 1


NABBJIN: hibit hibit 0720* Exhibit 9# n ? +7

? 5+.3

s ? $3

#0: µ 50 #a: µ = 50

NABBN 1. Befer to hibi hibitt 72*. 72*. The The test test statis statistic tic is is a. 0.11+ b. 0.*3+7 c. 21.$ d. 1.$ ANS: 

!TS: 1


$. $. Befer Befer to hibi hibitt 72*. 72*. The p2value is between a. 0.01 .01 to 0.0$ .0$5 b. 0.0$5 to 0.05 c. .05 to 0.1 d. 0.1 to 0.$ ANS: 

!TS: 1


*. Befer to hibit hibit 72*. If the test test is done done at the 5 level of si)nificance' si)nificance' the null null hypothesis hypothesis should a. not be re&e re&ect cted ed b. be re&ected c. Not enou) enou)h h informa information tion )iven to answer answer this -uestion -uestion.. alternatives is correct. d. None of these alternatives ANS: A

!TS: 1

NABBJIN: hibit hibit 0720+ Exhibit 9$


The mana)er of a )rocery store has taen a random sample of 100 customers. The avera)e len)th of time it too the customers in the sample to chec out was *.1 minutes with a standard deviation of 0.5 minutes. %e want to test to determine whether or not the mean waitin) time of all customers is si)nificantly more than * minutes. NABBN +. Befer to hibi hibitt 72+. 72+. The The test test statis statistic tic is is a. 1.7/ b. 1./+ c. $.00 d. 0.05/ ANS: ;

!TS: 1


5. 5. Befer Befer to hibi hibitt 72+. 72+. The p2value is between a. .005 to to .0 .01 b. .01 to .0$5 c. .0$5 to to .0 .05 d. .05 to .10 ANS: 

!TS: 1


/. Befer to hibit hibit 72+. 72+. At 75 confidence confidence'' it can be concluded concluded that the mean mean of the population population is a. si)n si)nif ific ican antl tly y )rea )reate terr than than * b. not si)nificantly si)nificantly )reater than * c. si)n si)nif ific ican antl tly y les lesss tha than n* d. si)ni si)nific ficant antly ly )reate )reaterr then then *.13 *.13 ANS: A

!TS: 1


NABBJIN: hibit hibit 07205 Exhibit 9% A random sample of 100 people was taen. i)hty2five of the people in the sample favored ;andidate A. %e are interested in determinin) whether or not the proportion of the population in favor of ;andidate A is si)nificantly more than 30. NABBN . Befer to hibi hibitt 725. 725. The The test test statis statistic tic is is a. 0.30 b. 0.05 c. 1.$5 d. $.00 ANS: ;

!TS: 1


3. 3. Befer Befer to hibi hibitt 725. 725. The p2value is a. 0.$11$ b. 0.05 c. 0.0$5 d. 0.105/ ANS: 

!TS: 1


7. Befer to hibit hibit 725. At 75 confidence' it can be concluded concluded that the proportion proportion of the the population population in favor of candidate A

a. b. c. d.

is si)ni si)nific ficant antly ly )rea )reater ter than than 30 30 is not si)nificantly si)nificantly )reater than 30 is si)ni si)nific ficant antly ly )rea )reater ter than than 35 35 is not not si)n si)nifi ifican cantly tly )reate )reaterr than than 35 35

ANS: 

!TS: 1


NABBJIN: hibit hibit 0720/ Exhibit 9& A random sample of 1/ students selected from the student body of a lar)e university had an avera)e a)e of $5 years and a standard deviation of $ years. %e want to determine if the avera)e a)e of all the students at the university is si)nificantly more than $+. Assume the distribution of the population of a)es is normal. NABBN 30. Befer to hibi hibitt 72/. 72/. The The test test statis statistic tic is is a. 1.7/ b. $.00 c. 1./+5 d. 0.05 ANS: 

!TS: 1


31. 31. Befer Befer to hibi hibitt 72/. 72/. The p2value is between a. .005 to to .0 .01 b. .01 to .0$5 c. .0$5 to to .0 .05 d. .05 to .10 ANS: ;

!TS: 1


3$. Befer to hibi hibitt 72/. At 75 75 confidence' confidence' it can can be concluded concluded that that the mean a)e a)e is a. not si)nif si)nifica icantl ntly y diff differe erent nt from from $+ b. si)nificantly different different from $+ c. si)n si)nif ific ican antl tly y less less tha than n $+ d. si)n si)nif ific ican antl tly y more more tha than n $+ ANS: 

!TS: 1


NABBJIN: hibit hibit 0720 Exhibit 9' A random sample of 1/ statistics eaminations eaminations from a lar)e population was taen. The avera)e score in the sample was 3./ with a variance of /+. %e are interested in determinin) whether the avera)e )rade of the population is si)nificantly more than 5. Assume the distribution of the population of )rades is normal. NABBN 3*. Befer to hibi hibitt 72. 72. The The test test statis statistic tic is is a. 0.+5 b. 1.30 c. *./ d. 3 ANS: 

!TS: 1


3+. 3+. Befer Befer to hibi hibitt 72. 72. The p2value is between a. .005 to to .0 .01 b. .01 to .0$5 c. .0$5 to to .0 .05 d. .05 to 0.1 ANS: ;

!TS: 1


35. Befer to hibit hibit 72. At 75 confidence' it can be concluded concluded that the avera)e )rade of the population population a. is not not si)n si)nifi ifican cantly tly )reate )reaterr than than 5 5 b. is si)nificantly si)nificantly )reater than 5 c. is not not si)n si)nifi ifican cantly tly )reate )reaterr than than 3./ 3./ d. is si)n si)nifi ifican cantly tly )reate )reaterr than than 3./ 3./ ANS: 

!TS: 1


NABBJIN: hibit hibit 07203 Exhibit 9( The avera)e )asoline price of one of the ma&or oil companies in urope has been D1.$5 per liter. Becently' the company has undertaen several efficiency measures in order to reduce prices. Eana)ement is interested in determinin) whether their efficiency measures have actually red)ced prices. A random sample of +7 of their their )as stations is selected selected and the avera)e price is determined to be D1.$0 per liter. urthermore' assume that the standard deviation of the population 4 6 is D0.1+. NABBN 3/. Befer to hibi hibitt 723. 723. The standard standard error error has a value value of a. 0.1+ b.  c. $.5 d. 0.0$ ANS: 

!TS: 1


3. Befer to hibit hibit 723. 723. The value value of the the test statis statistic tic for this this hypoth hypothesis esis test test is a. 1.7/ b. 1./+5 c. 2$.5 d. 21./+5 ANS: ;

!TS: 1


33. 33. Befer Befer to hibi hibitt 723. 723. The p2value for this problem is a. 0.+7*3 b. 0.00/$ c. 0.01$+ d. 0.05 ANS: 

!TS: 1

NABBJIN: hibit hibit 07207 Exhibit 99


The sales of a )rocery store store had an avera)e of D3'000 per day. day. The store introduced several advertisin) campai)ns in order to increase sales. To determine whether whether or not the advertisin) campai)ns have been effective in increasin) sales' sales' a sample of /+ days of sales was selected. It was found that the avera)e was D3'*00 per day. rom past information' it is nown that the standard deviation of the population is D1'$00. NABBN 37. Befer to to hibit hibit 727. The correct correct null hypo hypothesi thesiss for this this proble problem m is a. µ < 3000 b. µ > 3000 c. µ ? 3000 d. µ > 3$50 ANS: A

!TS: 1


70. Befer to hibi hibitt 727. 727. The value value of the test statistic statistic is a. $50 b. 3000 c. 3$50 d. $.0 ANS: 

!TS: 1


71. 71. Befer Befer to hibi hibitt 727. 727. The p-value is a. $.00 b. 0.7$ c. 0.0$$3 d. 0.5+5 ANS: ;

!TS: 1


PRO*LEM

1. The epartmen epartmentt of conomic conomic and ;ommunity ;ommunity evelopm evelopment ent 4;6 4;6 reported reported that in $007 $007 the avera)e number of new &obs created per county was +50. The department also provided the followin) followin) information re)ardin) a sample of 5 counties in $010. Co)nt+

radley Bhea Earion Jrundy Se-uatchie a. b. c. d.

,e- obs Created In "/!/ +10 +30 +0 +$3 +00

;ompute ;ompute the the sample sample avera)e avera)e and and the the standa standard rd deviat deviation ion for $010. %e want to determine whether whether there has been a si0ni1icant decrease in the avera)e number of &obs created. !rovide the null and the the alternative hypotheses. hypotheses. ;omp ;omput utee the the test test stat statis isti tic. c. ;ompute th the p2valueC and at 75 confidence' test the hypotheses. hypotheses. Assume the population is normally distributed.

ANS:

a. b. c. d.

? +$5 and s ? *$.++ 4rounded6 #o: µ = +50 #a: µ < +50 Test st statistic t ? ? 21.$+ P 2value 2value is between 0.05 and 0.1C do not re&ect # o. There is no evidence of a si)nificant si)nificant decrease.

!TS: 1


$. The ureau ureau of ,abor Statisti Statistics cs reported reported that that the avera)e yearly yearly income income of dentists dentists in the year year $007 was D110'000. A sample of 31 dentists' which was taen in $010' showed an avera)e yearly income income of D1$0'000. Assume the standard standard deviation deviation of the population of dentists in $010 is D*/'000. a. b. c.

%e want want to test test to determ determine ine if there there has has been been a si)nifica si)nificant nt increase in the avera)e yearly income of dentists. dentists. !rovide the null and the the alternative hypotheses. hypotheses. ;ompute the test statistic. statistic. etermi rmine the p2valueC and at 75 confidence' test the hypotheses.

ANS: a. #o: µ ≤ D110'000 #a: µ > D110'000 b. 8 ? $.5 c. p2value ? 0.00/$ Since the p2value ? 0.00/$ < 0.05' re&ect # o. Therefore' there has been a si)nificant si)nificant increase. !TS: 1


*. A tire manufacturer has been producin) tires with with an avera)e life epectancy epectancy of of $/'000 $/'000 miles. Now the company is advertisin) that its ne- tiresH life epectancy has has increased. In order to test the le)itimacy of the advertisin) campai)n' an independent testin) a)ency tested a sample of / of their tires and has provided the followin) data. Li1e Ex2ectanc+ 3In Tho)sands o1 Mi4es5 $3 $ $5 $3 $7 $5

a. b. c.

eterm etermine ine the the mean mean and and the the stan standa dard rd devia deviatio tion. n. At 77 confidence usin) usin) the critical value value approach' test to determine determine whether or not the tire company is usin) le)itimate advertisin). Assume the population is normally distributed. Bepe Bepeat at the the test test usin usin) ) the the p2value approach.

ANS: a. ? $' s ? 1./ b. #o: µ < $/000 #a: µ = $/000 Since t ? ? 1.+ < *.*/5' do not re&ect # o and conclude that there is insufficient evidence to support the manufacturerHs claim.

c.

p2value > 0.1C do not re&ect # o

!TS: 1


+. A producer of various inds of batteries has been producin) producin) KK si9e si9e batteries with a life life epectancy epectancy of 3 hours. ue to an improved production process' process' mana)ement believes that there has been an increase in the life epectancy of their KK si9e batteries. A sample of */ batteries showed an avera)e life of 33.5 hours. Assume from past information information that it is nown nown that the standard deviation of the population is 7 hours. a. b. c. d.

Jive Jive the the null null and and the the alte alterna rnativ tivee hypot hypothes heses. es. ;ompute the test statistic. statistic. At 77 77 confiden confidence ce usin) usin) the the critical critical value value appro approach' ach' test test mana)emen mana)ementHs tHs belief. belief. %hat is the p2value associated with the sample results( results( %hat is your conclusion based on the p2value(

ANS: a. #o: µ < 3 #a: µ = 3 b. c. d.

1.00 Sinc Sincee 8 ? 1 < $.* $.**' *' do not not re& re&ec ectt #o and conclude that there is insufficient evidence to support the corporationHs claim. p2value = 0.153C therefore do not re&ect # o

!TS: 1


5. Some people people who bou)ht bou)ht L2Jame )amin) )amin) systems complain complained ed about havin) havin) received received defective defective systems. The industry standard for such systems has been ninety2ei)ht percent non2defective systems. In a sample of 1$0 units sold' / units were defective. a. b. c. d.

;ompute ;ompute the the propo proportion rtion of defect defective ive items in the sample. sample. ;ompute the standard error of . At 75 confid confidence ence usin) usin) the the critical critical value value approach approach'' test to to see if the the percenta) percenta)ee of defective defective systems produced by L2Jame has eceeded the industry standard. Show that the p2value approach results in the same conclusion as that of part b.

ANS: a. b. c. d.

0.05 0.01$3 Test Test stati statisti sticc 8 ? $.*5 $.*5 = 1./+ 1./+5C 5C re&ect re&ect # oC the number of defects has eceeded the industry standard. p2value 4.007+6 < 0.05C re&ect # o.

!TS: 1


/. ;hoo ;hoo !aper ;ompany maes various types of paper products. products. "ne of their products products is a *0 mils thic paper. In order to ensure that the thicness of the paper meets the *0 mils specification' random cuts of paper are selected and the thicness of each cut is measured. A sample of $5/ cuts had a mean thicness of *0.* mils with a standard deviation of + mils.

a. b. c.

;ompu ;ompute te the stand standard ard error error of the mean. mean. At 75 confidence usin) usin) the critical value value approach' test to see if the mean thicness is si)nificantly more than *0 mils. Show th that th the p2value approach results in the same conclusion as that of part b.

ANS: a. b. c.

0.$5 Test statistics t ? 1.$ < 1./+5C do not re&ect # o. p2value 4.11516 is between 0.1 and 0.$C do not re&ect # o.

!TS: 1


. ,ast year' 50 of of ENE' Inc. Inc. employees were female. It is believed that there has been a reduction reduction in the percenta)e of females in the the company. This year' in a random sample sample of +00 employees' 130 were were female. a. b. c.

Jive Jive the the null null and and the the alte alterna rnativ tivee hypot hypothes heses. es. At 75 confidence usin) usin) the critical value value approach' determine if there has been a si)nificant reduction in the proportion of females. Show th that th the p2value approach results in the same conclusion as that of !art b.

ANS: a. b. c.

#o: p ≥ 0.5 #a: p < 0.5 Test statistic 8 ? 2$.0 2$.0 < 21./+5C re&ect # oC the proportion of female employees is si)nificantly less than 50. p2value ? 0.0$$3 < 0.05C re&ect # o.

!TS: 1


3. ,ast year' a soft drin manufacturer manufacturer had $1 of the maret. maret. In order to increase increase their portion of the maret' the manufacturer has introduced introduced a new flavor in their their soft drins. A sample of +00 individuals individuals participated in the taste taste test and 100 indicated indicated that they lie the the taste. %e are interested in determinin) if more than $1 of the population will lie the new soft drin. a. b. c. d.

Set up up the the null null and and the the alter alterna nativ tivee hypot hypothes heses. es. etermine the test statistic. statistic. etermi rmine the p2value. At 75 confid confidence' ence' test test to determine determine if if more than $1 $1 of the popula population tion will will lie the the new soft drin.

ANS: a. b. c. d.

#0: p 0.$1 #a: p = 0.$1 Test statistic 8 ? 1.7/ p2value ? 0.0$5 p2value ? 0.0$5 < .05C therefore' re&ect # oC more than $1 lie the new drin.

!TS: 1


7. In the past' past' the avera)e a)e a)e of employees employees of a lar)e corporatio corporation n has been +0 years. years. Becently' Becently' the company has been hirin) older individuals. In order to determine whether there has been an increase in the avera)e a)e of all the employees' a sample of /+ employees was selected. The avera)e a)e in the sample was +5 years with a standard deviation of 1/ years. ,et α ? .05. a. b. c.

State State the the null null and and the the alter alternat native ive hyp hypoth othese eses. s. ;ompute the test statistic. statistic. Msin) th the p2value approach' test to determine whether or not the mean a)e of all employees is si)nificantly more than +0 years.

ANS: a. b. c.

#0: µ +0 #a: µ = +0 t ? $.5 p2value 4.005136 is between .005 and .01C re&ect # 0

!TS: 1


10. The avera)e )asoline price price of one of the ma&or oil companies has been D$.$0 per )allon. )allon. ecause of cost reduction measures' it is believed that there has been a si)nificant red)ction in the avera)e price. In order to test this belief' we randomly selected a sample of */ of the companyHs )as stations and determined that the avera)e price for the stations in the sample was D$.1+. Assume that the standard deviation of the 2o2)4ation 4σ6 is D0.1$. a. b. c. d.

State State the the null null and and the the alter alternat native ive hyp hypoth othese eses. s. ;ompute the test statistic. statistic. %hat is the p2value associated with the above sample results( At 75 75 conf confid idenc ence' e' test test the the compa companyH nyHss claim. claim.

ANS: a. b. c. d.

#0: µ $.$0 #a: µ < $.$0 8 ? 2* p2value ? almost 9ero 40.001*6 p2value < .05C re&ect # 0C the avera)e price has been reduced.

!TS: 1


11. A sample of 31 account account balances balances of a credit credit company company showed showed an avera)e balance balance of D1'$00 D1'$00 with a standard deviation of D1$/. a.

ormulate ormulate the the hypothese hypothesess that can can be used used to determin determinee whether whether the mean mean of all all account account balances is si)nificantly si)nificantly different from D1'150. D1'150. b. ;ompute the test statistic. statistic. c. Msin) the p2value approach' what is your conclusion( ,et α ? .05. ANS: a.

#0: µ ? 1150 #a: µ ≠ 1150

b. c.

t ? *.5 p2value 4almost 9ero6 <.005C therefore' re&ect # 0

!TS: 1


1$. rom a populati population on of cans of coffee coffee mared mared K1$ ounces'K ounces'K a sample sample of 50 cans was was selected selected and the the contents of each can were wei)hed. The sample revealed a mean of 11.3 ounces with a standard deviation of 0.5 ounces. a. b. c.

ormulate ormulate the the hypothese hypothesess to test to see if the the mean of of the populat population ion is at at least least 1$ ounces. ounces. ;ompute the test statistic. statistic. Msin) the p2value approach' what is your conclusion( ,et α ? .05.

ANS: a. b. c.

#0: µ 1$ #a: µ < 1$ t ? 2$.3* p2value 4.00*+6 < .005C therefore' re&ect # 0

!TS: 1


1*. A lathe is set to cut bars bars of steel into into len)ths of / centimeters. The lathe is considered to be be in perfect ad&ustment if the avera)e len)th of the bars it cuts is / centimeters. A sample of 1$1 bars is selected randomly and measured. It is determined that the avera)e len)th of the bars in the sample is /.03 centimeters with a standard deviation of 0.++ centimeters. a. b. c.

ormulate ormulate the the hypothese hypothesess to determine determine whether whether or not the the lathe lathe is in perfec perfectt ad&ustmen ad&ustment. t. ;ompute the test statistic. statistic. Msin) the p2value approach' what is your conclusion( ,et α ? .05.

ANS: a. b. c.

#0: µ ? / #a: µ ≠ / t?$ p2value 4.0+5/6 is between 0.0$ and 0.05C therefore' re&ect # 0

!TS: 1


1+. Ahmadi' Inc. has been manufacturin) small automobiles automobiles that that have avera)ed 50 50 miles per )allon )allon of )asoline in hi)hway drivin). The company has developed a more efficient en)ine for its small cars and now advertises that its new small cars avera)e more than 50 miles per )allon in hi)hway drivin). An independent testin) service road2tested road2tested /+ of the automobiles. The sample showed an avera)e of 51.5 miles per )allon with a standard deviation of + miles per )allon. a. b. c.

ormulate ormulate the the hypothese hypothesess to determine determine whether whether or not not the manufactu manufacturerHs rerHs adverti advertisin) sin) campai) campai)n n is le)itimate. ;ompute the test statistic. statistic. %hat is the p2value associated with the sample results and what is your conclusion( ,et α ? . 05.

ANS: a. b. c.

#0: µ 50 #a: µ = 50 t?* p2value 4.00176 is less than .005C re&ect # 0

!TS: 1


15. A soft drin drin fillin) machine' when in perfect ad&ustment' fills fills the bottles with with 1$ ounces ounces of soft soft drin. A random sample of +7 bottles is selected' and the contents are measured. The sample yielded a mean content of 11.33 ounces with a standard deviation of 0.*5 ounces. a. b. c.

ormulate ormulate the the hypothese hypothesess to test to determine determine if if the machine machine is is in perfect perfect ad&ust ad&ustment. ment. ;ompute the value of the test statistic. ;ompute the p2value and )ive your conclusion re)ardin) the ad&ustment of the machine. ,et α ? .05.

ANS: a. b. c.

#0: µ ? 1$ #a: µ ≠ 1$ t ? 2$.+ p2value is between 0.01 and 0.0$5C therefore' re&ect # 0

!TS: 1


1/. KK si9e batterie batteriess produced produced by ENE ;orporatio ;orporation n have had a life epectancy epectancy of 3 hours. hours. ecause ecause of an improved production process' it is believed that there has been an increase in the life epectancy of its KK si9e batteries. A sample of */ batteries showed an avera)e life of 33.5 hours. Assume from past information that it is nown that the standard deviation of the 2o2)4ation is 7 hours. a. b. c.

ormul ormulate ate the hyp hypoth othese esess for for this this prob problem lem.. ;ompute the test statistic. statistic. %hat is the p2value associated with the sample results( %hat is your conclusion based on the p2value( ,et α ? .05.

ANS: a. b. c.

#0: µ 3 #a: µ = 3 8?1 p2value ? 0.153C therefore' do not re&ect # 0

!TS: 1


1. At a local local university' university' a sample of +7 evenin) evenin) students students was selected in order to determine determine whether whether the avera)e a)e of the evenin) students is si)nificantly different from $1. The avera)e a)e of the students in the sample was $* with a standard deviation of *.5. a. b.

ormul ormulate ate the hyp hypoth othese esess for for this this prob problem lem.. ;ompute the test statistic. statistic.

c.

etermine the p2value and test these hypotheses. ,et α ? .05.

ANS: a. b. c.

#0: µ ? $1 #a: µ ≠ $1 t?+ p2value is almost 9eroC therefore' re&ect # 0

!TS: 1


13. In order to determine the avera)e price of hotel rooms in Atlanta' a sample of /+ hotels was selected. selected. It was determined that the avera)e price of the rooms in the sample was D103.50 with a standard deviation of D1/. a. b. c.

ormulate ormulate the the hypothese hypothesess to determine determine whether whether or not not the avera)e avera)e room room price is si)nif si)nificant icantly ly different from D11$. ;ompute the test statistic. statistic. At 75 confidence usin) the p2value approach' test the hypotheses. ,et α ? 0.1.

ANS: a. b. c.

#0: µ ? 11$ #a: µ ≠ 11$ t ? 21.5 p2value is between 0.0$5 and 0.05C therefore' do not re&ect # 0

!TS: 1


17. Identify Identify the null null and alternativ alternativee hypotheses hypotheses for the follow followin) in) problems. problems. a.

The mana)er mana)er of of a restaurant restaurant believe believess that it it taes a custo customer mer less less than or or e-ual to to $5 minutes minutes to to eat lunch. b. conomists have stated stated that the mar)inal propensity propensity to consume consume is at least 70 out of every every dollar. c. It has been been stated stated that that 5 out of every 100 people people who who )o to the the movies movies on Saturda Saturday y ni)ht ni)ht buy popcorn. ANS: a. b. c.

#0: µ $5 #a: µ = $5 #0: p 0.7 #a: p < 0.7 #0: p ? 0.5 #a: p ≠ 0.5

!TS: 1


$0. A student believes that that the avera)e avera)e )rade on on the statistics statistics final final eamination eamination was 3. 3. A sample of */ final eaminations was taen. The avera)e )rade in the sample was 3*.7/ with a standard deviation of 1$.

a. b. c.

State State the the nul nulll and and alter alterna nativ tivee hypot hypothes heses. es. Msin) the critical value value approach' test the hypotheses hypotheses at the 5 level level of si)nificance. Msin) th the p2value approach' test the hypotheses at the 5 level of si)nificance.

ANS: a. b. c.

#0: µ ? 3 #a: µ ≠ 3 test statistic statistic t ? 21.5$' critical t ? $.0*C do not re&ect # 0 p2value is between .05 and 0.1C therefore' do not re&ect # 0

!TS: 1


$1. A carpet company advertises advertises that it will deliver your your carpet within within 15 days of purchase. A sample of +7 past customers is taen. The avera)e delivery time in the sample was 1/.$ days. The standard deviation of the 2o2)4ation 4σ6 is nown to be 5./ days. a. b. c.

State State the the nul nulll and and alter alterna nativ tivee hypot hypothes heses. es. Msin) the critical value approach' test to determine if their advertisement is le)itimate. ,et α ? .05. Msin) th the p2value approach' test the hypotheses at the 5 level of si)nificance.

ANS: a. b. c.

#0: µ 15 #a: µ = 15 test statistic statistic 8 ? 1.5 < 1./+5C therefore do not not re&ect # 0 o not re&ect #0C p2value is 4.5 2 .+**$6 ? 0.0//3

!TS: 1


$$. A sample of *0 cooies cooies is taen to test the claim that each cooie contains at at least 7 chocolate chips. chips. The avera)e number of chocolate chips per cooie in the sample was .3 with a standard deviation of *. a. b. c. d.

State State the the nul nulll and and alter alterna nativ tivee hypot hypothes heses. es. Msin) the critical value value approach' test the hypotheses hypotheses at the 5 level level of si)nificance. Msin) th the p2value approach' test the hypothesis at the 5 level of si)nificance. ;ompute ;ompute the probab probabilit ility y of a Type Type II error if if the true true number number of chocolat chocolatee chips chips per cooie cooie is 3.

ANS: a. b. c. d.

#0: µ 7 #a: µ < 7 test statistic statistic t ? 2$.170 < 21./77C re&ect # 0 re&ect #0C the p2value is between .01 to .0$5 A Type Type II error error has has not not been been comm committ itted ed sinc sincee # 0 was re&ected.

!TS: 1


$*. A )roup of youn) businesswomen wish to open a hi)h fashion fashion bouti-ue in a vacant store but only if the avera)e income of households in the area is at least D$5'000. A random sample of 7 households showed the followin) results. D$3'000 D$*'000 D$+'000

D$+'000 D$'000

D$/'000 D$/'000

D$5'000 D$$'000

Assume the population of incomes is normally distributed. a. b. c. d.

;ompu ;ompute te the the sample sample mean mean and and the the standa standard rd devia deviatio tion. n. State the hypotheses hypotheses for this problem. ;omp ;omput utee the the test test stat statis isti tic. c. At 75 75 con confi fide denc ncee usi usin) n) the the p2value approach' what is your conclusion(

ANS: a. b. c. d.

? $5'000 s ? 1'7*/.+7 #0: µ $5'000 #a: µ < $5'000 test est st stati atistic tic t ? 0 p2value ? 0.5C do not re&ect # 0' the bouti-ue should be opened.

!TS: 1


$+. Nancy believes believes that the the avera)e runnin) runnin) time of movies is e-ual to 1+0 minutes. A sample of + movies was taen and the followin) runnin) times were obtained. Assume the population of the runnin) times is normally distributed. 150 a. b. c. d.

150

130

10

;ompu ;ompute te the the sample sample mean mean and and the the standa standard rd devia deviatio tion. n. State the null and alternative alternative hypotheses. hypotheses. Msin) Msin) the critica criticall value value approach' approach' test test the hypoth hypotheses eses at the the 10 level level of si)ni si)nifican ficance. ce. Msin) the p2value approach' test the hypotheses at the 10 level of si)nificance.

ANS: a. b. c. d.

? 1/$.5 s ? 15 #0: µ ? 1+0 #a: µ ≠ 1+0 Be&ect #0C test statistic t ? * = $.*5* The p2value is between .05 to .10C Be&ect # 0

!TS: 1


$5. A student believes that no more than $0 4i.e.' $06 of the students who finish a statistics course )et an A. A random sample of 100 students was taen. Twenty2four percent of the students in the sample received AHs. a. b.

State State the the nul nulll and and alter alterna nativ tivee hypot hypothes heses. es. Msin) the critical value value approach' test the hypotheses hypotheses at the 1 level level of si)nificance.

c.

Msin) th the p2value approach' test the hypotheses at the 1 level of si)nificance.

ANS: a. b. c.

#0: ! 0.$ #a: ! = 0.$ o not re&ect #0C test statistic 8 ? 1 < $.** o not re&ect #0C p2value ? 0.153 = 0.01

!TS: 1


$/. An official of a lar)e national union union claims that the fraction fraction of women in the union is not si)nificantly different from one2half. Msin) the critical value approach and the sample information reported below' carry out a test of this statement. ,et α ? 0.05. sample si9e women men ANS: #0: ! ? 0.5 #a: ! ≠ 0.5

+00 1/3 $*$

Be&ect #0C test statistic 8 ? 2*.$ < 21.7/

!TS: 1


$. A law enforcement enforcement a)ent believes that at least 33 of the the drivers stopped on on Saturday ni)hts for speedin) are under the influence of alcohol. A sample of // drivers who were stopped for speedin) on a Saturday ni)ht was taen. i)hty percent of the drivers in the sample were under the influence of alcohol. a. b. c.

State State the the nul nulll and and alter alterna nativ tivee hypot hypothes heses. es. ;ompute the test statistic. statistic. Msin) th the p2value approach' test the hypotheses at the .05 level of si)nificance.

ANS: a. b. c.

#0: ! 0.33 #a: ! < 0.33 8 ? 2$ p2value ? 0.0$$3 < 0.05C re&ect # 0

!TS: 1


$3. Two thousand thousand number numberss are selected selected randoml randomlyC yC 7/0 were were even numbers numbers.. a. b. c.

State the the hypothese hypothesess to determine determine whether whether the the proportion proportion of odd odd numbers numbers is si)nific si)nificantl antly y different from 50. ;ompute the test statistic. statistic. At 70 70 con confi fide denc ncee usi usin) n) the the p2value approach' test the hypotheses.

ANS: a.

#0: ! ? 0.5

b. c.

#a: ! ≠ 0.5 8 ? 1.7 p2value ? .0*+ < 0.10C re&ect # 0

!TS: 1


$7. In the last last presidential presidential election' election' a national survey company claimed that that no more than 50 4i.e.' < 506 of all re)istered voters voted for the Bepublican candidate. In a random sample of +00 re)istered voters' $03 voted for the Bepublican candidate. a. b. c.

State State the the null null and and the the alter alternat native ive hyp hypoth othese eses. s. ;ompute the test statistic. statistic. At 75 75 conf confid iden ence ce'' comp comput utee the the p2value and test the hypotheses.

ANS: a. b. c.

#0: ! 0.5 #a: ! = 0.5 8 ? 0.3 p2value ? 0.$117 = 0.05C do not re&ect # 0.

!TS: 1


*0. An automobile automobile manufacturer stated that it will be willin) to mass produce produce electric2powered electric2powered cars if 6ore than *0 of potential buyers indicate they will purchase the newly desi)ned electric cars. In a sample of 500 potential buyers' 1/0 indicated that they would buy such a product. a. b. c. d.

State State the hyp hypoth othese esess for for this this prob problem lem ;ompute the standard error of . ;omp ;omput utee the the test test stat statis isti tic. c. At 75 confid confidence' ence' what what is your your conclusi conclusion( on( Should Should the the manufactu manufacturer rer produce produce the the new electric powered car(

ANS: a. b. c. d.

#0: ! 0.* #a: ! = 0.* 0.0$05 8 ? 0.73 p2value ? 0.1/*5 <0.05C do not re&ect # 0C no' the manufacturer should not produce the cars.

!TS: 1


*1. *1. It is said said that that 6ore males re)ister to vote in a national election than females. A research or)ani9ation selected a random sample of *00 re)istered voters and reported that 1/5 of the re)istered voters were male. a. b. c. d.

ormul ormulate ate the hyp hypoth othese esess for for this this prob problem lem.. ;ompute the standard error of . ;omp ;omput utee the the test test stat statis isti tic. c. Msin) the p2value approach' can you conclude that more males re)istered r e)istered to vote than females( ,et α ? .05.

ANS: a. b. c. d.

#0: ! 0.5 #a: ! = 0.5 0.0$37 8 ? 1.* p2value ? 0.0+13 < .05C re&ect # 0C yes' more males than females re)istered to vote.

!TS: 1


*$. ;onsider ;onsider the followin followin) ) hypoth hypothesis esis test: test: #o: µ ? 10 #a: µ ≠ 10 A sample of 31 provides a sample mean of 7.5 and a sample standard deviation of 1.3. a. b. c.

eterm etermine ine the standa standard rd erro errorr of the mean. mean. ;ompute the value of the test statistic. etermi rmine the p2valueC and at 75 confidence' test the above hypotheses.

ANS: a. b. c.

0.$ t ? 2$.5 p2value is between .01 and .0$ 4two tail test6C re&ect # 0

!TS: 1


**. ;onsider ;onsider the followin followin) ) hypoth hypothesis esis test: test: #o: µ 1+ #a: µ < 1+ A sample of /+ provides a sample mean of 1* and a sample standard deviation of +. a. b. c.


ANS: a. b. c.

0.5 t ? 2$ p2value is between .01 and .0$5C re&ect # 0

!TS: 1


*+. ;onsider ;onsider the followin followin) ) hypoth hypothesis esis test: test: #o: µ

+0

#a: µ < +0 A sample of +7 provides a sample mean of *3 and a sample standard deviation of . a. b. c.


ANS: a. b. c.

1 t ? 2$ p2value is between .0$5 and .05C re&ect # 0

!TS: 1


*5. ;onsider ;onsider the followin followin) ) hypoth hypothesis esis test: test: #o: µ *3 #a: µ = *3 Fou are )iven the followin) information obtained from a random sample of si observations. Assume the population has a normal distribution. 7 *3 +0 +$ *$ +/ +$

a. b. c. d. e.

;omp ;omput utee the the mean mean of the the sam sampl plee etermine the standard deviation deviation of the sample. sample. eterm etermine ine the standa standard rd erro errorr of the mean. mean. ;ompu ;ompute te the the valu valuee of the test test stati statisti stic. c. At 75 75 con confi fide denc ncee usi usin) n) the the p2value approach' test the above hypotheses.

ANS: a. b. c. d. e.

+0 +.* 1.7* 1.0*/ p2value is between 0.1 and 0.$C do not re&ect # 0.

!TS: 1


*/. ;onsider ;onsider the followin followin) ) hypoth hypothesis esis test: test: #o: ! 0.3 #a: ! = 0.3

A sample of +00 provided a sample proportion of 0.35*. a. b. c.

eterm etermine ine the the stand standard ard erro errorr of the the propor proportio tion. n. ;ompute the value of the test statistic. etermi rmine the p2valueC and at 75 confidence' test the above hypotheses.

ANS: a. b. c.

0.0$ 8 ? $./5 p2value ? 0.00+C re&ect # 0

!TS: 1


*. Fou are )iven )iven the followin) information obtained obtained from a random sample of 5 observations. observations. Assume the population has a normal distribution. $0

13

1

$$

13

Fou want to determine whether or not the mean of the population from which this sample was taen is si)nificantly less than $1. a. b. c. d.

State State the the null null and and the the alter alternat native ive hyp hypoth othese eses. s. ;ompute the standard error error of the mean. ete eterm rmin inee the the test test stat statis isti tic. c. etermi rmine th the p2value and at 70 confidence' test whether or not the mean of the population is si)nificantly less than $1.

ANS: a. b. c. d.

#0: µ $1 #a: µ < $1 0.37++ t ? 2$.$*/ p2value is between .0$5 and .05C re&ect # 0' the mean is si)nificantly less than $1.

!TS: 1


*3. ;onsider ;onsider the followin followin) ) hypoth hypothesis esis test: test: #o: p ? 0.5 #a: p ≠ 0.5 A sample of 300 provided a sample proportion of 0.53. a. b. c.

eterm etermine ine the the stand standard ard erro errorr of the the propor proportio tion. n. ;ompute the value of the test statistic. etermi rmine the p2value' and at 75 confidence' test the hypotheses.

ANS: a. b.

0.01/3 8 ? +.5*

c.

p2value is almost 9eroC re&ect # 0

!TS: 1


*7. Fou are )iven )iven the followin) followin) informa information tion obtained obtained from from a random sample sample of + observations observations.. $5

+

*$

5/

Fou want to determine whether or not the mean of the population from which this sample was taen is si)nificantly different from +3. 4Assume the population is normally distributed.6 a. b. c.

State State the the null null and and the the alter alternat native ive hyp hypoth othese eses. s. etermine the test statistic. statistic. etermi rmine the p2valueC and at 75 confidence test to determine whether or not the mean of the population is si)nificantly si)nificantly different different from +3.

ANS: a. b. c.

#0: µ ? +3 #a: µ ≠ +3 t ? 21.1* p2value is between 0.$ and 0.+ 4two 4 two tailed6C do not re&ect # 0.

!TS: 1


+0. ;onfirmed cases of %est Nile virus in birds for a sample sample of si counties in the state of Jeor)ia are shown below. Co)nt+ ;atoosa ;hattoo)a ade Jordon Eurray %aler

Cases / * * 5 * +

%e are interested in testin) the followin) hypotheses re)ardin) these data: #0: µ * #a: µ = * a. b. c. d.

;ompute ;ompute the the mean mean and and the the standar standard d deviatio deviation n of the sample sample.. ;ompute the standard error error of the mean. ete eterm rmin inee the the test test stat statis isti tic. c. etermi rmine th the p2value and at 75 confidence' test the hypotheses.

ANS: a. b. c. d.

+ and and 1.$/5 .$/5 4rou 4round nded ed66 0.51/+ t ? 1.7+ .7+ 4rou 4round nded ed66 2value is between 0.05 and 0.1C re&ect # 0 and conclude that the mean of the population is p si)nificantly more than *.

!TS: 1


+1. A sample of /+ account account balances from a credit credit company showed an avera)e daily balance of D1'0+0. The standard deviation of the population is nown to be D$00. D$00. %e are interested in determinin) determinin) if the mean of all account balances 4i.e.' population mean6 is si)nificantly different different from D1'000. a. b. c. d. e.

evelop evelop the appropria appropriate te hypothese hypothesess for for this this problem. problem. ;ompute the test statistic. statistic. ;ompute the p2value. Msin) the p2value approach at 75 confidence' test the above hypotheses. Msin) Msin) the criti critical cal value value approach approach at 75 75 confiden confidence' ce' test test the hypothese hypotheses. s.

ANS: a. #o: µ = 1000 #a: µ ≠ 1000 b. 1./0 c. 0.107/ d. The p2value ? 0.107/' which is lar)er than α ? 0.05 475 confidence6. #ence' the null null hypothesis is not re&ectedC and we conclude that there is not sufficient evidence to indicate that the advertisin) campai)ns have been effective. e. In !art b' the Z statistic statistic was computed computed and its value was 1./0. 1./0. Since 1./0 is between 21.7/ 21.7/ and 1.7/' the null hypothesis cannot be re&ectedC and we conclude that there is no evidence that the mean is si)nificantly different from D1'000. !TS: 1


+$. ;onsider ;onsider the followin followin) ) hypoth hypotheses eses test. test. #o: µ ≥ 30 #a: µ < 30 A sample of 1$1 1$1 provided a sample mean of .*. .*. The population standard standard deviation is nown to be 1/.5. a. b. c.

;ompu ;ompute te the the valu valuee of of the the test test statis statistic tic.. etermine the p2valueC and at 7*. confidence' test the above hypotheses. Msin) Msin) the criti critical cal value value approach approach at 7*. 7*. confiden confidence' ce' test test the the hypothese hypotheses. s.

ANS: a. 8 ? 21.3 b. p2value ? 0.0*57 < 0.0/*' re&ect # o c. test statistic Z ? ? 21.3 < 8.0/* ? 21.5*' re&ect # o !TS: 1


+*. Automobiles manufactured by the fficiency ;ompany ;ompany have been avera)in) avera)in) +$ miles per per )allon of )asoline in hi)hway drivin). drivin). It is believed that its new automobiles avera)e 6ore than +$ miles per )allon. An independent independent testin) service service road2tested */ */ of the automobiles. automobiles. The sample showed showed an avera)e of +$.3 miles per )allon with a standard deviation of 1.$ miles per )allon. a.

%ith a 0.05 0.05 level of si)nif si)nificanc icancee usin) the the critical critical value value approach approach'' test to determin determinee whether whether or not the new automobiles actually do avera)e more than +$ miles per )allon.

b.

%hat is the p2value associated with the sample results( results( %hat is your conclusion based on the p2value(

ANS: a. #o: µ < +$ #a: µ = +$ Since t ? ? +.0 = 1./70' re&ect # o and conclude that the new cars avera)e more than +$ miles per )allon. b. p2value < 0.005' therefore re&ect # o 4area to the ri)ht of t ? ? +.0 is almost 9ero6 !TS: 1


++. The avera)e startin) salary salary of students students who who )raduated from colle)es of usiness in $007 was D+3'+00. D+3'+00. A sample of 100 )raduates of "/!/ showed an avera)e startin) startin) salary of D50'000. Assume the standard deviation of the population population is nown to be D3'000. %e want to determine whether or not there has been a si)nificant increase in the startin) salaries. a. b. c. d. e.

State State the the null null and alter alterna nativ tivee hypoth hypothese esess to be teste tested. d. ;ompute the test statistic. statistic. The null null hypoth hypothesis esis is is to be be tested tested at 75 75 confiden confidence. ce. etermine etermine the the critical critical value value for for this test. %hat %hat do you you con concl clud ude( e( ;omp ;omput utee the the p2va p2valu lue. e.

ANS: a. #o: µ ≤ +3'+00 #a : µ > +3'+00 b. Test Statistic 8 ? $.0 $.0 c. ;ritical 8 ? 1. 1./+ d. Be&ect #o and conclude that there has been a si)nificant increase. e. !2value ? .0$$3 !TS: 1

T"!: #ypothesis Testin)

+5. The avera) avera)ee price price of homes homes sold sold in the M.S. M.S. in the past year was was D$$0'000. D$$0'000. A random sample of 31 homes sold this year showed showed an avera)e price of D$10'000. It is nown that the the standard deviation of the population is D*/'000. D*/'000. At 75 confidence test to determine if there has been a si)nificant decrease in the avera)e price homes. a. b. c. d. e.

State State the the null null and alter alterna nativ tivee hypoth hypothese esess to be teste tested. d. ;ompute the test statistic. statistic. eterm etermine ine the critic critical al valu valuee for for this this test test.. %hat %hat do you you con concl clud ude( e( ;omp ;omput utee the the p2va p2valu lue. e.

ANS: a. #o: µ ≥ $$0'000 #a : µ < $$0'000 b. Test statistic 8 ? 2$.5 2$.5 c. ;rit ;ritiical cal 8 ? 21./ 21./+ + d. Be&ect #o and conclude that there has been a si)nificant decrease. e. !2value ? 0.00 .00/$

!TS: 1

T"!: #ypothesis Testin)

Chapter 9 Testbank (1)

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