Chapter PVII, Problem 27RE

To determine

To create a confidence interval to test the clinic’s claim that the typical weight loss is ten pounds.

Answer to Problem 27RE

We are $95\%$ confident that the average weight loss for the clinic is between $8.24\text{ and }10.06$ .

Explanation of Solution

In this question, we have to find the confidence interval to test the clinic’s claim that the typical weight loss is ten pounds.Thus, to find the confidence interval for mean we will use the calculator $\text{TI}-89$ . In the STAT Intsmenu, choose $2:$

TInterval. Specify whether you are using data stored in a list or whether you will enter the mean, standard deviation, and sample size. You must also specify the desired level of confidence. The list for the data is:

Pounds Lost
9.5
13
9
10
11
9
5
9
12.5
6
9.5
9
8
7.5
10
7
8
10.5
10.5
9

Thus, by using the calculator $\text{TI}-89$ , the confidence interval will be as:

  $(8.24,10.06)$ .

So, we conclude that based on these data, we are $95\%$ confident that the average weight loss for the clinic is between $8.24\text{ and }10.06$ and the clinic’s claim is plausible.