To help your restaurant marketing campaign target the right age levels, you want to find out if there is a statistically significant difference, on the average, between the age of your customers and the age of the general population in town, 43.1 years.  A random sample of 50 customers shows an average of 38.1 years with a sample standard deviation of 16.2 years.

(a) Identify the null and research hypotheses for a 2-sided test using both words and math symbols

(b) Perform a 2-sided test at the 5% significance level and describe the result (use method of finding t (stat) and compare it to the appropriate t value from t-table

(c) Perform a 2-sided test at the 1% significant level for this problem and describe the result (same method as part b)

(d) Calculate a 95% confidence interval for the average age of all customers.  Verify that your answer to part b would be the same if it was based on this confidence interval

(e) Calculate a 99% confidence interval for the average age of all customers.  Verify that your answer to part c would be the same if it was based on this confidence interval