A Single Population Mean using the Student t Distribution · 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 $\bar{X}$ 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.
(c) Calculate the error bound.
(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 Statistics 2e · §8.2 A Single Population Mean using the Student t Distribution · Exercise 28