States that rely on sales tax for revenue to fundeducation, publicsafety, and other programs often end up with budget surpluses during economic growth periods(when people spend more on consumergoods) and budget deficits during recessions(when people spend less on consumergoods). 18 small retailers in a state with a growing economy were recently sampled. The sample showed a mean increase of $2040 in additional sales tax revenue collected per retailer compared to the previous quarter. The sample standard deviation is $418. Complete parts a through d below.

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

The standard error is $

(Round to two decimal places asneeded.)

b) What happens to the accuracy of an estimate when an interval is constructed using a smaller samplesize?

The standard error and width of the interval (increases or decreases),

which means that the accuracy of the interval (decreases or increases).

c) Find and interpret a 95% confidence interval.

( $ , )

(Round to one decimal place asneeded.)

d) How does the margin of error for the interval compare to the margin of error for a confidence interval of 53 smallretailers, which yielded the same sample mean increase and standarddeviation? The 95% confidence interval with 53 retailers is ($2505.1,$2734.9).

The margin of error for the confidence interval created with 18 small retailers is $________

, while the margin of error for the confidence interval created with 53 retailers is $________

(Round to one decimal place asneeded.)

Which sample would a state budget plannerprefer? Why?

A.

The planner would prefer the confidence interval created with 18 retailers because it has less error and greateraccuracy, since state expenditure decisions are based on the sample estimates.

B.

The planner would prefer the confidence interval created with 53 retailers because it has less error and greateraccuracy, since state expenditure decisions are based on the sample estimates.

C.

The planner would prefer the confidence interval created with 53 retailers because it has greaterrange, since state budget planners want to be as likely as possible that the interval contains the actual mean increase.

D.

The planner would prefer the confidence interval created with 18 retailers because it has greaterrange, since state budget planners want to be as likely as possible that the interval contains the actual mean increase.