Test Hypotheses Regarding the Difference of Two Independent Means
-Find the standardized test statistic, t, to test the hypothesis that $\mu _ { 1 } \mu _ { 2 }$. Two samples are randomly selected and come from populations that are normal. The sample statistics are given below.
$$\begin{array} { l l }
\mathrm { n } _ { 1 } = 18 & \mathrm { n } _ { 2 } = 13 \
\overline { \mathrm { x } } 1 = 680 & \overline { x _ { 2 } } = 665 \
\mathrm {~s} _ { 1 } = 40 & \mathrm {~s} _ { 2 } = 25
\end{array}$$
A) $1.282$
B) $3.271$
C) $2.819$
D) $1.865$

Question

Test Hypotheses Regarding the Difference of Two Independent Means
-Find the standardized test statistic, t, to test the hypothesis that $\mu _ { 1 } > \mu _ { 2 }$. Two samples are randomly selected and come from populations that are normal. The sample statistics are given below.
$$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 18 & \mathrm { n } _ { 2 } = 13 \
\overline { \mathrm { x } } 1 = 680 & \overline { x _ { 2 } } = 665 \
\mathrm {~s} _ { 1 } = 40 & \mathrm {~s} _ { 2 } = 25
\end{array}$$
A) $1.282$
B) $3.271$
C) $2.819$
D) $1.865$

Quizplus · Accepted Answer

The correct answer is A because the standardized test statistic, t, is calculated as:$$t = \frac{(\overline{x}_1 - \overline{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}}$$Since the population standard deviations are unknown, we use the sample standard deviations as estimates:$$t = \frac{(680 - 665) - (0 - 0)}{\sqrt{\frac{40^2}{18} + \frac{25^2}{13}}} = 1.282$$

Test Hypotheses Regarding the Difference of Two Independent Means -Find μ1>μ2\mu _ { 1 } > \mu _ { 2 }μ1​>μ2​

Test Hypotheses Regarding the Difference of Two Independent Means
-Find $\mu _ { 1 } > \mu _ { 2 }$