Sample standard deviation (s)
a. Compute the test statistic t.
b. Compute the degree of freedom for the test statistic t.
c. What is the rejection rule using the p-value approach and α = 0.05
d. What is the p-value?
e. Based on the rejection rule from c., what is your conclusion of the hypothesis?
f. Use the above data to construct a 95% confidence interval for the difference of the population means.
Note that the population standard deviations are not known and therefore you cannot use the formula in Section 10.1. Use those in Section 10.2 instead.
2. Responses from a customer satisfaction survey for two stores of a local hardware chain were recorded in the attached BUSI1013-Two Independent Samples A.xls file. These responses, in the form of a satisfaction score, are taken from a random sample of customers who shopped recently at the two stores and are recorded on a scale of 1 to 10. The chain wants to use this data to test the research (alternative) hypothesis that the mean satisfaction score for the two branches is not the same. The null hypothesis is that the mean satisfaction score for the two branches is the same. (10 points)
a. What are the sample mean satisfaction score and the sample standard deviation for the two branches?
b. Compute the test statistic t used to test the hypothesis.
c. Compute the degree of freedom for the test statistic t.
d. Can the chain conclude that the customer satisfaction level at the two stores is different? Use the critical-value approach and α = 0.05 to conduct the hypothesis test.
e. Construct a 95% confidence interval for the difference of the satisfaction scores for the two stores.
3. Use the data in and description of BUSI1013-Case.xls to answer this question. (4 points for each part; 8 points total)
a. Perform a statistical test to see whether the average deposits of members before the pilot are different between the two regions.
b. Construct a 95% confidence interval for the difference of the two regions in average loans of members before the pilot.