8.2 Exercise 30

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.

1. 1. $\bar{x}$ = __________
   2. $s_{x}$ = __________
   3. n = __________
   4. n – 1 = __________
2. Define the random variable $X$ in words.
3. Define the random variable $\overset{-}{X}$ in words.
4. Which distribution should you use for this problem? Explain your choice.
5. Construct a 95% confidence interval for the population mean length of time.
   1. State the confidence interval.
   2. Sketch the graph.
6. What does it mean to be “95% confident” in this problem?