Test Hypotheses Regarding the Difference of Two Independent Means
-Find the standardized test statistic to test the hypothesis that $\mu _ { 1 } \neq \mu _ { 2 }$. Two samples are randomly selected from each population. The sample statistics are given below. Use $\alpha = 0.02$.
$$\begin{array} { l l }
\mathrm { n } _ { 1 } = 51 & \mathrm { n } _ { 2 } = 38 \
\overline { \mathrm { x } } 1 = 8.6 & \overline { \mathrm { x } } 2 = 9 \
\mathrm {~s} 1 = 0.76 & \mathrm {~s} _ { 2 } = 0.51
\end{array}$$
A) $- 2.97$
B) $- 1.82$
C) $- 2.12$
D) $- 2.32$

Question

Test Hypotheses Regarding the Difference of Two Independent Means
-Find the standardized test statistic to test the hypothesis that $\mu _ { 1 } \neq \mu _ { 2 }$. Two samples are randomly selected from each population. The sample statistics are given below. Use $\alpha = 0.02$.
$$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 51 & \mathrm { n } _ { 2 } = 38 \
\overline { \mathrm { x } } 1 = 8.6 & \overline { \mathrm { x } } 2 = 9 \
\mathrm {~s} 1 = 0.76 & \mathrm {~s} _ { 2 } = 0.51
\end{array}$$
A) $- 2.97$
B) $- 1.82$
C) $- 2.12$
D) $- 2.32$

Quizplus · Accepted Answer

The standardized test statistic is:$$z = \frac{(\overline{x}_1 - \overline{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}}$$Since the population standard deviations are unknown, we use the sample standard deviations as estimates:$$z = \frac{(8.6 - 9) - 0}{\sqrt{\frac{0.76^2}{51} + \frac{0.51^2}{38}}} = -2.97$$Therefore, the correct choice is A.

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 $\mu _ { 1 } \neq \mu _ { 2 }$