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 $\alpha = 0.05$.
$$\begin{array} { l l }
\mathrm { n } _ { 1 } = 100 & \mathrm { n } _ { 2 } = 125 \
\overline { \mathrm { x } } 1 = 505 & \overline { \mathrm { x } } 2 = 490 \
\mathrm {~s} _ { 1 } = 45 & \mathrm {~s} _ { 2 } = 25
\end{array}$$
A) 2.98
B) 2.81
C) 1.86
D) 0.91

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 $\alpha = 0.05$.
$$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 100 & \mathrm { n } _ { 2 } = 125 \
\overline { \mathrm { x } } 1 = 505 & \overline { \mathrm { x } } 2 = 490 \
\mathrm {~s} _ { 1 } = 45 & \mathrm {~s} _ { 2 } = 25
\end{array}$$
A) 2.98
B) 2.81
C) 1.86
D) 0.91

Quizplus · Accepted Answer

The standardized test statistic for comparing two means ($\mu_1 > \mu_2$) can be calculated using the formula:$$Z = \frac{\overline{x}_1 - \overline{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}$$Plugging in the given values:$$Z = \frac{505 - 490}{\sqrt{\frac{45^2}{100} + \frac{25^2}{125}}} = \frac{15}{\sqrt{\frac{2025}{100} + \frac{625}{125}}} = \frac{15}{\sqrt{20.25 + 5}} = \frac{15}{\sqrt{25.25}} = \frac{15}{5.025} \approx 2.98$$

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