Find the standardized test statistic to test the hypothesis that $\mu _ { 1 } = \mu _ { 2 }$. Two samples are randomly selected from each population. The sample statistics are given below. Use $\alpha = 0.05$.
$$\begin{array} { l l }
\mathrm { n } _ { 1 } = 40 & \mathrm { n } _ { 2 } = 35 \
\overline { \mathrm { x } } 1 = 18 & \overline { x _ { 2 } } = 19 \
\mathrm {~s} _ { 1 } = 2.5 & \mathrm {~s} _ { 2 } = 2.8
\end{array}$$
A) -1.6
B) -0.8
C) -2.6
D) -1.0

Question

Find the standardized test statistic to test the hypothesis that $\mu _ { 1 } = \mu _ { 2 }$. Two samples are randomly selected from each population. The sample statistics are given below. Use $\alpha = 0.05$.
$$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 40 & \mathrm { n } _ { 2 } = 35 \
\overline { \mathrm { x } } 1 = 18 & \overline { x _ { 2 } } = 19 \
\mathrm {~s} _ { 1 } = 2.5 & \mathrm {~s} _ { 2 } = 2.8
\end{array}$$
A) -1.6
B) -0.8
C) -2.6
D) -1.0

Quizplus · Accepted Answer

The standardized test statistic is calculated as:$$z = \frac{(\overline{x}_1 - \overline{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}}$$Since we are testing the hypothesis that $\mu_1 = \mu_2$, we have $\mu_1 - \mu_2 = 0$. Plugging in the given values, we get:$$z = \frac{(18 - 19) - 0}{\sqrt{\frac{2.5^2}{40} + \frac{2.8^2}{35}}} = -1.6$$Therefore, the standardized test statistic is -1.6, which corresponds to choice A.

Find the Standardized Test Statistic to Test the Hypothesis That μ1=μ2\mu _ { 1 } = \mu _ { 2 }μ1​=μ2​

Find the Standardized Test Statistic to Test the Hypothesis That $\mu _ { 1 } = \mu _ { 2 }$