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.
$\begin{array} { l l }
\mathrm { n } _ { 1 } = 50 & \mathrm { n } _ { 2 } = 60 \
\overline { \mathrm { x } } _ { 1 } = 25 & \overline { \mathrm { x } } _ { 2 } = 23 \
\mathrm {~s} _ { 1 } = 1.5 & \mathrm {~s} _ { 2 } = 1.9
\end{array}$
A) $( 1.364,2.636 )$
B) $( 1.572,2.987 )$
C) $( 1.723,3.012 )$
D) $( 1.919,3.142 )$

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.
$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 50 & \mathrm { n } _ { 2 } = 60 \
\overline { \mathrm { x } } _ { 1 } = 25 & \overline { \mathrm { x } } _ { 2 } = 23 \
\mathrm {~s} _ { 1 } = 1.5 & \mathrm {~s} _ { 2 } = 1.9
\end{array}$
A) $( 1.364,2.636 )$
B) $( 1.572,2.987 )$
C) $( 1.723,3.012 )$
D) $( 1.919,3.142 )$

Quizplus · Accepted Answer

The confidence interval for the difference between two means, $\mu_1 - \mu_2$, can be calculated using the formula: $\overline{x}_1 - \overline{x}_2 \pm z \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$, where $z$ is the z-score corresponding to the desired confidence level (for 95%, $z \approx 1.96$), $\overline{x}_1$ and $\overline{x}_2$ are the sample means, $s_1$ and $s_2$ are the sample standard deviations, and $n_1$ and $n_2$ are the sample sizes. Plugging in the given values, the correct interval is $(1.364, 2.636)$.

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

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