A Single Population Mean Using the Student's t-Distribution · Exercise 28

A pharmaceutical company makes a drug used during surgery. It is assumed that the distribution for the length of time the drug lasts is approximately normal. Researchers in a hospital used the drug on a random sample of nine patients. The effective period of the antibiotic drug 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 percent 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 percent confident in this problem?

OpenStax, Statistics · §8.2 A Single Population Mean Using the Student's t-Distribution · Exercise 28