A Single Population Mean Using the Student's t-Distribution · Exercise 26

A random survey of enrollment at 35 community colleges across the United States yielded the following figures: 6,414, 1,550, 2,109, 9,350, 21,828, 4,300, 5,944, 5,722, 2,825, 2,044, 5,481, 5,200, 5,853, 2,750, 10,012, 6,357, 27,000, 9,414, 7,681, 3,200, 17,500, 9,200, 7,380, 18,314, 6,557, 13,713, 17,768, 7,493, 2,771, 2,861, 1,263, 7,285, 28,165, 5,080, 11,622. Assume the underlying population is normal.
(a) (a) $\bar{x}$ = __________
(b) $s_x$ = __________
(c) n = __________
(d) n – 1 = __________
(b) Define the random variables $X$ and $\bar{X}$ in words.
(c) Which distribution should you use for this problem? Explain your choice.
(d) Construct a 95 percent confidence interval for the population mean enrollment at community colleges in the United States.
(a) State the confidence interval.
(b) Sketch the graph.
(c) Calculate the error bound.
(e) What will happen to the error bound and confidence interval if 500 community colleges are surveyed? Why?

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Statistics · §8.2 A Single Population Mean Using the Student's t-Distribution · Exercise 26