Chapter PVI, Problem 15RE

(a)

To determine

To find out what kind of sampling design were surveyed.

Answer to Problem 15RE

Stratified sampling method is used.

Explanation of Solution

It is given in the question that a Gallup telephone poll of $1240$ teen conducted in $2001$ found that boys were more likely than girls to play computer games, by a margin of error of $\text{77\% to 65\%}$ . And equal number of boys and girls were surveyed. Thus, as the data is divided into the two strata, that is according to the gender, boys and girls so we can say that the sampling design used in this context is stratified sampling method.

(b)

To determine

To give a $95\%$ confidence interval for the difference in game playing by gender.

Answer to Problem 15RE

We are $95\%$ confident that the difference in game playing by gender lie between $7\%\text{ and 17\%}$ .

Explanation of Solution

It is given in the question that a Gallup telephone poll of $1240$ teen conducted in $2001$ found that boys were more likely than girls to play computer games, by a margin of error of $\text{77\% to 65\%}$ . And equal number of boys and girls were surveyed.Thus, to find the confidence interval for proportion we will use the calculator $\text{TI}-89$ . To calculate a confidence interval for a population proportion: Go to the STAT Intsmenu and select $6:2-$ PropZInt. Enter the observed counts and the sample size for both the samples. Specify a confidence level. Calculate the interval. So, we have,

  $\begin{array}{l}{p}_1=0.77\\ n_1=1240\\ p_2=0.65\\ n_2=1240\end{array}$

And $\alpha =0.05$ so by using the calculator $\text{TI}-89$ , the confidence interval will be as:

  $(0.07,0.17)$

So, we are $95\%$ confident that the difference in game playing by gender lie between $7\%\text{ and 17\%}$ .

(c)

To determine

To explain does your confidence interval suggest that among all teens a higher percentage of boys than girls play computer games.

Answer to Problem 15RE

Yes, our confidence interval suggest that among all teens a higher percentage of boys than girls play computer games.

Explanation of Solution

It is given in the question that a Gallup telephone poll of $1240$ teen conducted in $2001$ found that boys were more likely than girls to play computer games, by a margin of error of $\text{77\% to 65\%}$ .So, we are $95\%$ confident that the difference in game playing by gender lie between $7\%\text{ and 17\%}$ . Thus, our confidence interval suggest that among all teens a higher percentage of boys than girls play computer games because the entire interval lies above zero.