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 with a sample standard deviation of 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. Discuss potential sources of error or bias in the fast-food restaurant example.

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