Background: A fast food restaurant claims that the average wait time for a drive-thru order is 3 minutes. The restaurant manager wants to test this claim with a sample of customers. Task: You have been hired as a data analyst to help the restaurant manager with hypothesis testing and confidence intervals.

1. Formulate the null and alternative hypotheses for this situation.

2. If a random sample of 50 customers produces a sample mean wait time of 2.8 minutes, and the population standard deviation is 0.4 minutes, calculate the test statistic using a z-value.

3. Calculate the p-value for this test and interpret the results at a significance level of 0.05.

4. Determine the critical value for a one-tailed test with a significance level of 0.05 and compare it with the calculated z-value. What is your conclusion?

5. How would decreasing the sample size from 50 to 25 affect your conclusion?

Explain.

6. Provide two examples of situations or industries where hypothesis testing and confidence intervals could be useful, and briefly explain why.

Include a full report that will include abstract, introduction, theory, results and discussion. conclusions and references.