The makers of a soft drink want to identify the average age of its consumers. A sample of 55 consumers was taken. The average age in the sample was 21 years with a standard deviation of 4 years.

a. Calculate a point estimate for the average age of the company's consumers.

b. Calculate the margin of error for a 95% confidence interval for the average age of the company's consumers. (Use the fact that the 97.5th percentile of a t distribution with 54 degrees of freedom is 2.005.)

c. Calculate a 95% confidence interval for the average age of the company's consumers.

d. Interpret your 95% confidence interval. Be specific.

e. Suppose the company believes the average age of its consumers is 22. Use your confidence interval from part (c) to challenge that belief using a hypothesis test with significance level =0.05. (State the hypotheses, test decision, and conclusion.)