State budgets, part 2. Suppose the state in Exercise 27 sampled 16 small retailers instead of 51, and for the sample of 16, the sample mean increase again equaled $2350 in additional sales tax revenue collected per retailer com- pared to the previous quarter. Also assume the sample standard deviation = $425.

a) What is the standard error of the mean increase in sales tax revenue collected?

b) What happens to the accuracy of the estimate when the interval is constructed using the smaller sample size?

c) Find and interpret a 95% confidence interval.

d) How does the margin of error for the interval constructed in Exercise 27 compare with the margin of error constructed in this exercise? Explain statistically how sample size changes the accuracy of the constructed interval. Which sample would you prefer if you were a state budget planner? Why?