In order to estimate the difference between the average hourly wages of employees of two branches of a department store, the following data have been gathered. $\begin{array}{lll}
& \text { Downtown Store } & \text { North Mall Store } \
\text { Sample size } & 25 & 20 \
\text { Sample mean }& \$ 9 & \$ 8 \
\text { Sample standard deviation } & \$ 2 & \$ 1
\end{array}$ A 95% interval estimate for the difference between the two population means is
A) .071 to 1.929.
B) .226 to 1.774.
C) 1.09 to 4.078.
D) 1.078 to 2.922.

Question

In order to estimate the difference between the average hourly wages of employees of two branches of a department store, the following data have been gathered. $\begin{array}{lll}
& \text { Downtown Store } & \text { North Mall Store } \
 \text { Sample size } & 25 & 20 \
\text { Sample mean }& \$ 9 & \$ 8 \
\text { Sample standard deviation } & \$ 2 & \$ 1
\end{array}$   A 95% interval estimate for the difference between the two population means is
A) .071 to 1.929.
B) .226 to 1.774.
C) 1.09 to 4.078.
D) 1.078 to 2.922.

Quizplus · Accepted Answer

The correct answer is A because the 95% confidence interval for the difference between the two population means is:$(\bar{x}_1 - \bar{x}_2) \pm t_{\alpha/2, n_1 + n_2 - 2} \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$where $\bar{x}_1$ and $\bar{x}_2$ are the sample means, $s_1$ and $s_2$ are the sample standard deviations, $n_1$ and $n_2$ are the sample sizes, and $t_{\alpha/2, n_1 + n_2 - 2}$ is the critical value from the t-distribution with $n_1 + n_2 - 2$ degrees of freedom and a significance level of $\alpha/2$.Plugging in the values from the question, we get:$(\bar{x}_1 - \bar{x}_2) \pm t_{0.025, 43} \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$$= (9 - 8) \pm 2.021 \sqrt{\frac{2^2}{25} + \frac{1^2}{20}}$$= 1 \pm 2.021 \sqrt{0.168}$$= 1 \pm 2.021 \times 0.41$$= 1 \pm 0.828$$= (0.172, 1.828)$Therefore, the 95% confidence interval for the difference between the two population means is $0.172$ to $1.828$.

In Order to Estimate the Difference Between the Average Hourly