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.
$$\begin{array} { l l }
\mathrm { n } _ { 1 } = 18 & \mathrm { n } _ { 2 } = 13 \
\overline { \mathrm { x } } 1 = 425 & \overline { \mathrm { x } _ { 2 } } = 410 \
\mathrm {~s} _ { 1 } = 40 & \mathrm {~s} _ { 2 } = 25
\end{array}$$
A) 1.282
B) 3.271
C) 2.819
D) 1.865

Question

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.
$$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 18 & \mathrm { n } _ { 2 } = 13 \
\overline { \mathrm { x } } 1 = 425 & \overline { \mathrm { x } _ { 2 } } = 410 \
\mathrm {~s} _ { 1 } = 40 & \mathrm {~s} _ { 2 } = 25
\end{array}$$
A) 1.282
B) 3.271
C) 2.819
D) 1.865

Quizplus · Accepted Answer

The correct choice is A because the standardized test statistic, $t$, to test the hypothesis that $\mu _ { 1 } > \mu _ { 2 }$ is calculated as follows:$$t = \frac { ( \overline { x } _ { 1 } - \overline { x } _ { 2 } ) - ( \mu _ { 1 } - \mu _ { 2 } ) } { \sqrt { \frac { s _ { 1 } ^ { 2 } } { n _ { 1 } } + \frac { s _ { 2 } ^ { 2 } } { n _ { 2 } } } }$$Substituting the given values, we get:$$t = \frac { ( 425 - 410 ) - ( 0 ) } { \sqrt { \frac { 40 ^ { 2 } } { 18 } + \frac { 25 ^ { 2 } } { 13 } } } = 1.282$$Therefore, the standardized test statistic, $t$, is 1.282.

Find the Standardized Test Statistic ttt , to Test the Hypothesis That

Find the Standardized Test Statistic $t$ , to Test the Hypothesis That