Test Hypotheses Regarding the Difference of Two Independent Means
-Find the standardized test statistic, t, to test the hypothesis that $\mu _ { 1 } \neq \mu _ { 2 }$. Two samples are randomly selected and come from populations that are normal. The sample statistics are given below.
$$\begin{array} { l l }
\mathrm { n } _ { 1 } = 11 & \mathrm { n } _ { 2 } = 18 \
\overline { \mathrm { x } } 1 = 5.1 & \overline { \mathrm { x } } 2 = 5.5 \
\mathrm {~s} 1 = 0.76 & \mathrm {~s} _ { 2 } = 0.51
\end{array}$$
A) $\mathbf { - 1 . 5 4 6 }$
B) $- 1.821$
C) $- 2.123$
D) $- 1.326$

Question

Test Hypotheses Regarding the Difference of Two Independent Means
-Find the standardized test statistic, t, to test the hypothesis that $\mu _ { 1 } \neq \mu _ { 2 }$. Two samples are randomly selected and come from populations that are normal. The sample statistics are given below.
$$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 11 & \mathrm { n } _ { 2 } = 18 \
\overline { \mathrm { x } } 1 = 5.1 & \overline { \mathrm { x } } 2 = 5.5 \
\mathrm {~s} 1 = 0.76 & \mathrm {~s} _ { 2 } = 0.51
\end{array}$$
A) $\mathbf { - 1 . 5 4 6 }$
B) $- 1.821$
C) $- 2.123$
D) $- 1.326$

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:$$t = \frac{(5.1 - 5.5) - (0 - 0)}{\sqrt{\frac{0.76^2}{11} + \frac{0.51^2}{18}}} = -1.546$$

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

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