State What the Given Confidence Interval Suggests About the Two

question 127

Multiple Choice

State what the given confidence interval suggests about the two population means.
-A researcher was interested in comparing the amount of time spent watching television by women and by men. Independent simple random samples of 14 women and 17 men were selected, and each person was asked how many hours he or she had watched television during the previous week. The summary statistics are as follows.

$\begin{array}{l|l}\text { Women } & \text { Men } \\\hline \overline{\mathrm{x}}_{1}=12.6 \mathrm{hrs} & \overline{\mathrm{x}}_{2}=14.0 \mathrm{hrs} \\\mathrm{s}_{1}=3.9 \mathrm{hrs} & \mathrm{s}_{2}=5.2 \mathrm{hrs} \\\mathrm{n}_{1}=14 & \mathrm{n}_{2}=17\end{array}$

The following $99 \%$ confidence interval was obtained for $\mu_{1}-\mu_{2}$ , the difference between the mean amount of time spent watching television for women and the mean amount of time spent watching television for men: $-6.33 \mathrm{hrs}<\mu_{1}-\mu_{2}<3.53 \mathrm{hrs}$ .
$\text { What does the confidence interval suggest about the nonulation means? }$

• A) The confidence interval limits include 0 which suggests that the two population means might be equal. There does not appear to be a significant difference between the mean amount of time spent watching television for women and the mean amount of time spent watching television for men.
• B) The confidence interval includes only positive values which suggests that the mean amount of time spent watching television for women is larger than the mean amount of time spent watching television for men.
• C) The confidence interval includes only negative values which suggests that the mean amount of time spent watching television for women is smaller than the mean amount of time spent watching television for men.
• D) The confidence interval limits include 0 which suggests that the two population means are unlikely to be equal. There appears to be a significant difference between the mean amount of time spent watching television for women and the mean amount of time spent watching television for men.

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