Problem
We are interested in studying whether consumers comfort with vacationing on cruise ships has returned to pre-pandemic levels. Suppose we have survey data from a random sample of consumers, both taken in the Phoenix area. The first sample was taken in the fall of 2019. From a random sample of 100 customers, 74 said that they would feel comfortable taking a cruise . A second sample was taken in the summer of 2022. In that sample of 100 customers 59 said they would be comfortable taking a cruise.
1. Perform a hypothesis test at alpha=.05 level of significance to determine of the proportion of consumers comfortable with cruising has changed since 2019. List the null and alternative hypotheses, calculate the standard error of the difference between the two proportions, the z-test score, z- critical score(s), and pvalue. Lastly, draw a complete hypothesis testing conclusion.
2. Calculate a 95% confidence interval estimate of the difference in the proportions of customers that are comfortable with cruises.
3. Does your confidence interval from part b support a conclusion that the proportion of consumers comfortable with cruising has changed since 2019? Why or why not?