Construct and Interpret Confidence Intervals Regarding the Difference of Two Independent Means
-Construct a $95 \%$ confidence interval for $\mu _ { 1 } - \mu _ { 2 }$. Two samples are randomly selected from each population.
The sample statistics are given below.
$\begin{array} { l l }
\mathrm { n } _ { 1 } = 40 & \mathrm { n } _ { 2 } = 35 \
\overline { \mathrm { x } } 1 = 12 & \overline { \mathrm { x } } 2 = 13 \
\mathrm {~s} _ { 1 } = 2.5 & \mathrm {~s} _ { 2 } = 2.8
\end{array}$
A) $( - 2.209,0.209 )$
B) $( - 2.001 , - 1.873 )$
C) $( - 1.968,1.561 )$
D) $( - 1.673,1.892 )$

Question

Construct and Interpret Confidence Intervals Regarding the Difference of Two Independent Means
-Construct a $95 \%$ confidence interval for $\mu _ { 1 } - \mu _ { 2 }$. Two samples are randomly selected from each population.
The sample statistics are given below.
$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 40 & \mathrm { n } _ { 2 } = 35 \
\overline { \mathrm { x } } 1 = 12 & \overline { \mathrm { x } } 2 = 13 \
\mathrm {~s} _ { 1 } = 2.5 & \mathrm {~s} _ { 2 } = 2.8
\end{array}$
A) $( - 2.209,0.209 )$
B) $( - 2.001 , - 1.873 )$
C) $( - 1.968,1.561 )$
D) $( - 1.673,1.892 )$

Quizplus · Accepted Answer

The confidence interval for the difference between two means is calculated using the formula: $\overline{x}_1 - \overline{x}_2 \pm t_{\alpha/2} \cdot \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$. Given the sample sizes and standard deviations, the correct interval is calculated to be $(-2.209, 0.209)$, indicating the range within which the true difference between the population means $\mu_1 - \mu_2$ is expected to lie with 95% confidence.

Construct and Interpret Confidence Intervals Regarding the Difference of Two 95%95 \%95%

Construct and Interpret Confidence Intervals Regarding the Difference of Two $95 \%$