Test Hypotheses Regarding the Difference of Two Independent Means
-Find the standardized test statistic, $t$, to test the hypothesis that $\mu _ { 1 }

Question

Test Hypotheses Regarding the Difference of Two Independent Means
-Find the standardized test statistic, $t$, to test the hypothesis that $\mu _ { 1 } < \mu _ { 2 }$. Two samples are randomly selected and come from populations that are normal. The sample statistics are given below.
$$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 15 & \mathrm { n } _ { 2 } = 15 \
\overline { \mathrm { x } } 1 = 22.02 & \overline { \mathrm { x } } 2 = 24.57 \
\mathrm {~s} 1 = 2.9 & \mathrm {~s} _ { 2 } = 2.8
\end{array}$$
A) $- 2.450$
B) $- 3.165$
C) $- 1.667$
D) $- 0.669$

Quizplus · Accepted Answer

The standardized test statistic $t$ for comparing two independent means is calculated using the formula:$$ t = \frac{\overline{x}_1 - \overline{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} $$Plugging in the given values:$$ t = \frac{22.02 - 24.57}{\sqrt{\frac{2.9^2}{15} + \frac{2.8^2}{15}}} = \frac{-2.55}{\sqrt{\frac{8.41}{15} + \frac{7.84}{15}}} = \frac{-2.55}{\sqrt{1.077}} \approx -2.450 $$

Test Hypotheses Regarding the Difference of Two Independent Means -Find ttt

Test Hypotheses Regarding the Difference of Two Independent Means
-Find $t$