27. State budgets. States that rely on sales tax for revenue to fund education, public safety, and other programs often end up with budget surpluses during economic growth periods

(when people spend more on consumer goods) and budget deficits during recessions (when people spend less on consumer goods). Fifty-one small retailers in a state with a growing economy were recently sampled. The sample showed a mean increase of $2350 in additional sales tax revenue collected per retailer compared to the previous quarter. The sample standard deviation

a) Find a 95% confidence interval for the mean increase in sales tax revenue.

b) What assumptions have you made in this inference? Do you think the appropriate conditions have been satisfied?

c) Explain what your interval means and provide an example of what it does not mean.