Chapter PVI, Problem 8RE

To determine

To give a $95\%$ confidence interval for the difference in the rates for males and females and be sure to check the assumptions that support your chosen procedure and interpret your interval.

Answer to Problem 8RE

We are $95\%$ confident that the difference in the rates for males and females lie between $-15.98\text{ and 0}\text{.051}$ .

Explanation of Solution

It is given in the question that a study of the health behavior of school-aged children asked a sample of $15$ -years-olds in several different countries if they had been drunk at least twice. Let us check the assumptions as:

Random condition: It is satisfied as the sample is assumed to be taken randomly.

Independent condition: It is satisfied as the sample is independent from each other as the data is based on gender.

Normal condition: It is satisfied as it is assumed the sample is normally distributed.

So, all the assumptions are satisfied. Thus, to find the confidence interval for mean we will use the calculator $\text{TI}-89$ . In the STAT Intsmenu, choose $4:2-$ SampTInt. You must specify if you are using data stored in two lists or if you will enter the means, standard deviations, and sizes of both samples. You must also indicate whether to pool the variances (when in doubt, say no) and specify the desired level of confidence. Thus, the list of the data is as:

Female	Male
63	71
63	72
59	58
62	51
58	52
56	53
44	53
31	49
36	49
42	42
40	40
41	37
29	42
31	36
23	47
23	44
22	43
21	39
29	34
22	36
22	36
25	32
20	32
20	29
21	24
16	25
10	18

Thus, by using the calculator $\text{TI}-89$ , the test statistics and the P-value is as:

  $\begin{array}{l}t=-2.00\\ P=0.0514\\ \text{Margin of error}=8.014\end{array}$

And the confidence interval will be as:

  $(-15.98,0.051)$ .

So, we conclude that we are $95\%$ confident that the difference in the rates for males and females lie between $-15.98\text{ and 0}\text{.051}$ .