Test Hypotheses Regarding the Difference of Two Independent Means
-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 $\alpha = 0.05$.
$$\begin{array} { l l }
\mathrm { n } _ { 1 } = 100 & \mathrm { n } _ { 2 } = 125 \
\overline { \mathrm { x } } 1 = 545 & \overline { \mathrm { x } _ { 2 } } = 530 \
\mathrm {~s} 1 = 45 & \mathrm {~s} _ { 2 } = 25
\end{array}$$
A) $2.98$
B) $2.81$
C) $1.86$
D) $0.91$

Question

Test Hypotheses Regarding the Difference of Two Independent Means
-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 $\alpha = 0.05$.
$$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 100 & \mathrm { n } _ { 2 } = 125 \
\overline { \mathrm { x } } 1 = 545 & \overline { \mathrm { x } _ { 2 } } = 530 \
\mathrm {~s} 1 = 45 & \mathrm {~s} _ { 2 } = 25
\end{array}$$
A) $2.98$
B) $2.81$
C) $1.86$
D) $0.91$

Quizplus · Accepted Answer

The standardized test statistic for comparing two means is 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: $$Z = \frac{545 - 530}{\sqrt{\frac{45^2}{100} + \frac{25^2}{125}}} = \frac{15}{\sqrt{\frac{2025}{100} + \frac{625}{125}}} = \frac{15}{\sqrt{20.25 + 5}} = \frac{15}{\sqrt{25.25}} = \frac{15}{5.025} \approx 2.98.$$

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