Question
Please show work
In a survey conducted by a department store, 8 randomly chosen married couples were asked to give a satisfaction index (0-100) based on their latest visits. The results of the survey are displayed below: Assume that the satisfaction indices for husbands and wives are normally distributed. Consider first the data for husbands only. Suppose the population standard deviation of satisfaction index for husbands is 24. Find a point estimate for the mean satisfaction index for husbands in the population. Find a 99% two-sided CI for the mean satisfaction index for husbands in the population. Provide a sound interpretation of the CI you obtained above. Would the CI computation you performed in be meaningful if the satisfaction index for husbands is not normally distributed? Explain. Can the CI you obtained in be used to test whether the mean satisfaction index for husbands in the population is different from 60? If yes, explain what the conclusion of the test would be and specify the significance level that is used. If not, explain why the CI cannot be used for that purpose. For the same test as in part above, find the power of the test if the true mean satisfaction index for husbands in the population is in fact 75. Suppose it is claimed that the mean satisfaction index for husbands in the population is less than 65. Test the claim using the rejection region approach at 5% significance level. Interpret the result of the test. Find the p-value associated with the test in part above. Provide a sound interpretation of the p-value you obtained above.
Explanation / Answer
(i) Mean = 64.25
(ii) Lower 99%
36.52
Upper 99%
91.98
(iii) We can be 99% certain that the true population mean falls within the range of
36.52 to 91.98.
(iv) We used t-test in order to calculate the confidence interval of population mean. The t-test
requires normality assumption. If normalirty assumption is violated then the above
confidence interval will not be meaningful.
(v) Yes, we can use the confidence interval in order to check whether the mean satisfaction of
male is different from 60.
H0 : population mean = 60 against HA : Population mean ? 60
The p