Question

2. 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 bills, he used StatKey to construct a 95% bootstrap confidence interval of [0.018, 0.292] for r. [24 points]

A. What if the manager wanted to do 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.

3. A researcher wants to compare the means of 4 different groups. What procedure(s) should he use and why? [12 points]

Answer 1

Result:

A).

In hypothesis testing, we are testing whether the population correlation is significantly different from 0.

We are testing whether there any significant correlation between the amount of customers bill and the percent that they tip.

B).

The confidence interval (0.018, 0.292) does not contain 0 value. We reject the null hypothesis.

We conclude that there is significant correlation between the amount of customers bill and the percent that they tip.

C).

In confidence interval we report that the actual correlation falls in the interval with the 95% confidence.

But in the hypothesis testing we conclude testing whether the population correlation is significantly different from 0.

We use hypothesis testing when we want to do a comparison with a pre-specified hypothesis and significance level. We use confidence intervals to describe sample with mean or correlation.

2).

ANOVA procedure should be used.

Analysis of Variance (ANOVA) is a statistical method used to test differences between more than two group means.