A Confidence Interval When the Population Standard Deviation Is Unknown and Small Sample Case · 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% confidence interval for the population mean enrollment at community colleges in the United States.
(a) State the confidence interval.
(b) Sketch the graph.
(e) What will happen to the error bound and confidence interval if 500 community colleges were surveyed? Why?

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

OpenStax, Introductory Business Statistics 2e · §8.2 A Confidence Interval When the Population Standard Deviation Is Unknown and Small Sample Case · Exercise 26