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

Question

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

Quizplus · Accepted Answer

The 95% confidence interval for the difference in means $\mu_1 - \mu_2$ is calculated using the formula: $(\overline{x}_1 - \overline{x}_2) \pm t^* \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$. With the given data, the interval is approximately (-2.209, 0.209).

Construct a 95% Confidence Interval For μ1−μ2\mu _ { 1 } - \mu _ { 2 }μ1​−μ2​

Construct a 95% Confidence Interval For $\mu _ { 1 } - \mu _ { 2 }$