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.
$$\begin{array} { l l }
\mathrm { n } _ { 1 } = 14 & \mathrm { n } _ { 2 } = 12 \
\overline { \mathrm { x } } 1 = 10 & \overline { \mathrm { x } } 2 = 11 \
\mathrm {~s} _ { 1 } = 2.5 & \mathrm {~s} _ { 2 } = 2.8
\end{array}$$
A) $- 0.954$
B) $- 0.915$
C) $- 1.558$
D) $- 0.909$

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.
$$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 14 & \mathrm { n } _ { 2 } = 12 \
\overline { \mathrm { x } } 1 = 10 & \overline { \mathrm { x } } 2 = 11 \
\mathrm {~s} _ { 1 } = 2.5 & \mathrm {~s} _ { 2 } = 2.8
\end{array}$$
A) $- 0.954$
B) $- 0.915$
C) $- 1.558$
D) $- 0.909$

Quizplus · Accepted Answer

The standardized test statistic $t$ is calculated using the formula for two independent samples:$$t = \frac{\overline{x}_1 - \overline{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}$$Plugging in the given values:$$t = \frac{10 - 11}{\sqrt{\frac{2.5^2}{14} + \frac{2.8^2}{12}}} = \frac{-1}{\sqrt{\frac{6.25}{14} + \frac{7.84}{12}}} = \frac{-1}{\sqrt{0.446 + 0.653}} = \frac{-1}{\sqrt{1.099}} = \frac{-1}{1.048} = -0.954$$

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

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