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Statistics solution for Small sample test:
For problem 2 & 4, answer the questions: ( a) Is this a one- or two- tailed test? ( b) What is the decision rule? ( c) What is the value of the test statistic? ( d) What is your decision regarding H 0 ? ( e) What is the p- value? Interpret it. 1) A sample of 36 observations is selected from a normal population. The sample mean is 12, and the population standard deviation is 3. Conduct the following test of hypothesis using the .02 significance level.
Ho: u <
10
H1: u >
10
Answer the questions: ( a) Is this a one- or two- tailed test? ( b) What is the decision rule? ( c) What is the value of the test statistic? ( d) What is your decision regarding H 0 ? ( e) What is the p- value? Interpret it.
Solution:
a) It is one-tailed test. b) Decision Rule – If Z-statistics is greater than critical value, reject the null hypothesis or accept otherwise. c) Test Statistics Z = (X-bar - µ)/ (σ/√n) = (12 – 10)/ (3/√36) =4 d) Using Z-tables, the critical value is Z (0.02) = 2.054 Since test statistics is greater than critical value, we reject Ho. e) P [Z > 4] = 0.000 Since p-value is less than 0.02, we reject Ho.
2) A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the foll owing test of hypoth-esis using the .03 significance level.
Ho: u >
220
H1: u <
220
answer the questions: ( a) Is this a one- or two- tailed test? ( b) What is the decision rule? ( c) What is the value of the t he test statistic? ( d) What is your decision regarding H 0 ? ( e) What is the p- value? Interpret it.
Solution:
a) It is one-tailed test. b) Decision Rule – If Z-statistics is greater than critical value, reject the null hypothesis or accept otherwise. c) Test Statistics Z = (X-bar - µ)/ (σ/√n) = (215 – 220)/ (15/√64) = -2.67 d) Using Z-tables, the critical value is Z (0.03) = -1.88 Since test statistics is less than critical value, we fail to reject Ho. e) P [Z < -1.88] = 0.0301 Since p-value is greater than 0.03, we fail to reject Ho.
