1. Now you will estimate the proportion of customers that will recommend the restaurant to others with 95% confidence interval. Tips: There is no function in Excel that can do it for you, so you need to calculate all values by yourself.
(a) Obtain and interpret a 95% confidence interval for the proportion of customers that will recommend the restaurant to others.
(b) What are the assumptions required to make the inferences in part (a) valid? Are the assumptions met in this case? Explain briefly
. 4. Now you will examine the change in the proportion of customers that will recommend the restaurant to others between peak hours and non-peak hours.
(a) Is there evidence that the restaurant owner has seen a change in the proportion of customers that will recommend the restaurant to others between peak hours and non-peak hours? Obtain a contingency table (using the PivotTable feature) of the count of recommendations and not recommendations by peak hours. Paste the table into your report.
(b) Refer to the output in part (a) to answer the following questions: What percent of customers that would recommend the restaurant came during peak hours? What percent of customers that would recommend the restaurant didn’t come during peak hours?
(c) Carry out the appropriate two-sample proportion test at the 5% significance level to answer the question. Paste the corresponding output into your report. In particular, state the null and alternative hypotheses, report the value of the test statistic, its distribution under the null hypothesis, and the p-value of the test. State your conclusions.
(d) Obtain and interpret a 95% confidence interval for the difference in the proportion of customers that will recommend the restaurant to others between peak hours and non-peak hours. Paste the output into your report. What is the estimated difference in the proportions? Is the interval consistent with the conclusion reached in part (a)?
(e) Are the assumptions for inference in parts (a) and (b) met in this case? Refer to theory to answer the question.
(f) Is there evidence that the restaurant owner has seen a change in the proportion of customers that will recommend the restaurant to others between peak hours and non-peak hours? Carry out the appropriate chi-square test for homogeneity at the 5% significance level to answer the question. Paste the corresponding output into your report. In particular, state the null and alternative hypotheses, report the value of the test statistic, its distribution under the null hypothesis, and the p-value of the test. State your conclusions.
(g) What is the relationship between the tests in parts (a) and (d)? Particularly, comment on the relationship between their test statistic values, p-values, and conclusions.
5. Now you will examine the relationship between customers’ preference section of the menu and their recommendation of the restaurant. Using 𝛼 = 0.01, carry out an appropriate test to test if there is a relationship between customers’ preference section of the menu and their recommendation of the restaurant. State the null and alternative hypotheses, report the value of the test statistic, its distribution under the null hypothesis, and the p-value of the test. State your conclusions
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