Question

Confidence Intervals & Hypothesis Tests

The manager of a restaurant wants to know if there is a correlation between the amount of a customer’s bill and the percent that they tip. In other words, as people spend more money, do they tend to tip at different rates? With data from a random sample of 157 receipts, he used StatKey to construct a 95% bootstrap confidence interval for r. The results were: [0.018, 0.292].

A. If the manager wanted to conduct a hypothesis test instead, what would be the appropriate null and alternative hypotheses?

B. Based on the 95% confidence interval, would you expect the manager to reject or fail to reject the null hypothesis at the 0.05 alpha level? Explain your reasoning.

C. Using this scenario, compare and contrast confidence intervals and hypothesis testing. List at least one similarity and at least one difference.

Answer 1

a) H0: there is no correlation between the amount of a customer’s bill and the percent that they tip

H1: there is a correlation between the amount of a customer’s bill and the percent that they tip

b) Zero is not contain in the given confidence interval. i.e. the populatin correlation coefficient value will be lies between (0.018 and 0.292). so we reject H0

c) Thus we conclude that there is a correlation between the amount of a customer’s bill and the percent that they tip