A Confidence Interval When the Population Standard Deviation Is Unknown and Small Sample Case · Exercise 28

A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample of nine patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.7; 2.8; 3.0; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4.

(a) (a) $\bar{x}$ = __________
(b) $s_x$ = __________
(c) n = __________
(d) n – 1 = __________
(b) Define the random variable $X$ in words.
(c) Define the random variable $\stackrel{-}{X}$ in words.
(d) Which distribution should you use for this problem? Explain your choice.
(e) Construct a 95% confidence interval for the population mean length of time.
(a) State the confidence interval.
(b) Sketch the graph.
(f) What does it mean to be “95% confident” in this problem?

This is an open-ended exercise: its source gives no single answer.

OpenStax, Introductory Business Statistics 2e · §8.2 A Confidence Interval When the Population Standard Deviation Is Unknown and Small Sample Case · Exercise 28