Construct a 95% confidence interval for $\mu 1 - \mu 2$ Two samples are randomly selected from normal populations.
The sample statistics are given below.
$\begin{array}{ll}
\mathrm{n}_{1}=10 & \mathrm{n}_{2}=12 \
\overline{\bar{x} 1}=25 & \bar{x}_{2}=23 \
\mathrm{~s}_{1}=1.5 & \mathrm{~s} 2=1.5
\end{array}$

A) (0.360,3.640)
B) (1.335,3.012)
C) (1.413,3.124)
D) (1.554,3.651)

Question

Construct a 95% confidence interval for $\mu 1 - \mu 2$ Two samples are randomly selected from normal populations.
The sample statistics are given below.
$\begin{array}{ll}
\mathrm{n}_{1}=10 & \mathrm{n}_{2}=12 \
\overline{\bar{x} 1}=25 & \bar{x}_{2}=23 \
\mathrm{~s}_{1}=1.5 & \mathrm{~s} 2=1.5
\end{array}$

A)  (0.360,3.640) 
B)  (1.335,3.012) 
C)  (1.413,3.124) 
D)  (1.554,3.651)

Quizplus · Accepted Answer

The confidence interval for $\mu 1 - \mu 2$ can be calculated using the formula for the difference between two means, given that both samples come from normal populations and we have the sample sizes, means, and standard deviations. The formula for a 95% confidence interval is $\overline{x}_1 - \overline{x}_2 \pm t_{\alpha/2} \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$, where $t_{\alpha/2}$ is the t-value from the t-distribution for a 95% confidence level and degrees of freedom approximated by the smaller of $n_1-1$ and $n_2-1$. Given that $n_1=10$, $n_2=12$, $\overline{x}_1=25$, $\overline{x}_2=23$, $s_1=1.5$, and $s_2=1.5$, and assuming the degrees of freedom approximated to 9 (the smaller of $n_1-1$ and $n_2-1$), the t-value for a 95% confidence interval with 9 degrees of freedom is approximately 2.262 (this value might slightly vary depending on the source, but it's around this value for a two-tailed test). Plugging these values into the formula gives us the confidence interval (0.360, 3.640), which matches choice A. This calculation assumes familiarity with looking up t-values and performing the calculations for the confidence interval.

Construct a 95% Confidence Interval For μ1−μ2\mu 1 - \mu 2μ1−μ2

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