Apply the pooled t-interval procedure to obtain the required confidence interval. You may assume that the assumptionsfor using the procedure are satisfied.
-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.
$\begin{array} { r | r }
\text { Women } & \text { Men } \
\hline \bar{ x } _ { 1 } = 12.0 & \bar{ x } _ { 2 } = 17.3 \
\mathrm {~s} _ { 1 } = 4.8 & \mathrm {~s} _ { 2 } = 4.8 \
\mathrm { n } _ { 1 } = 14 & \mathrm { n } _ { 2 } = 17
\end{array}$
Determine a $95 \%$ confidence interval for the difference between the mean weekly television watching times of women and men.
A)$- 8.24$ to $- 2.36$ hours
B) $- 8.84$ to $- 1.76$ hours
C) $- 8.97$ to $- 1.63$ hours
D) $- 9.14$ to $- 1.46$ hours

Question

Apply the pooled t-interval procedure to obtain the required confidence interval. You may assume that the assumptionsfor using the procedure are satisfied.
-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. 
$\begin{array} { r | r } 
\text { Women } & \text { Men } \
\hline \bar{ x } _ { 1 } = 12.0 & \bar{ x } _ { 2 } = 17.3 \
\mathrm {~s} _ { 1 } = 4.8 & \mathrm {~s} _ { 2 } = 4.8 \
\mathrm { n } _ { 1 } = 14 & \mathrm { n } _ { 2 } = 17
\end{array}$
Determine a $95 \%$ confidence interval for the difference between the mean weekly television watching times of women and men.  
A)$- 8.24$ to $- 2.36$ hours
B) $- 8.84$ to $- 1.76$ hours
C) $- 8.97$ to $- 1.63$ hours
D) $- 9.14$ to $- 1.46$ hours

Quizplus · Accepted Answer

To calculate the 95% confidence interval for the difference between two means with pooled variance, we use the formula: $\bar{x}_1 - \bar{x}_2 \pm t_{\alpha/2} \cdot \sqrt{\frac{s_p^2}{n_1} + \frac{s_p^2}{n_2}}$, where $s_p^2 = \frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1 + n_2 - 2}$ is the pooled variance. Given $\bar{x}_1 = 12.0$, $\bar{x}_2 = 17.3$, $s_1 = s_2 = 4.8$, $n_1 = 14$, and $n_2 = 17$, we calculate the pooled variance and then the confidence interval. The correct interval, based on these calculations, is $- 8.84$ to $- 1.76$ hours, which matches option B.

Apply the Pooled T-Interval Procedure to Obtain the Required Confidence