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 normal populations.
The sample statistics are given below.
$\begin{array} { l l } \mathrm { n } _ { 1 } = 10 & \mathrm { n } _ { 2 } = 12 \ \overline { \mathrm { x } } 1 = 25 & \overline { \mathrm { x } } 2 = 23 \ \mathrm {~s} _ { 1 } = 1.5 & \mathrm {~s} _ { 2 } = 1.9 \end{array}$
A) $( 0.360,3.640 )$
B) $( 1.335,3.012 )$
C) $( 1.413,3.124 )$
D) $( 1.554,3.651 )$

Question

Quizplus · Accepted Answer

The confidence interval for the difference between two independent means, assuming normal populations and using the formula for two samples, is calculated as follows: $\overline{x}_1 - \overline{x}_2 \pm t_{\alpha/2} \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$. Given the sample sizes, means, and standard deviations, and using a t-distribution (since population standard deviations are unknown and sample sizes are small), the calculation results in a 95% confidence interval of approximately $(0.360, 3.640)$.

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

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