1.(a) A grocery store determines that a coupon program is worthwhile if they can get more than 30% of their customers to use the program. They take a sample of 1,000 customers and within that sample 320 customers use coupons that are given to them. Use the hypothesis testing framework to provide a recommendation to the company.

1.State the null and alternative hypothesis.

2.Calculate the test statistics, include the formula used in the calculation.

3.State the reference distribution.

4.Derive the p-value using the test statistic and reference distribution, includ- ing a probability statement.

5.Use the p-value along with your null and alternative hypothesis to reach a final conclusion. Conclusion should be in the context of the problem. Don't just state generically "Reject the null, accept the alternative" or "We fail to reject the null".

(b) To do the previous problem correctly, you had to rely on the CLT. Explain why it is reasonable to use the CLT for the previous problem.