$$\begin{array}{l}
\text { In testing the equality of the two means below, what is the test statistic? (Use the unequal variances }\
\begin{array} { | l | c | c | }
\hline & \text { Sample 1 } & \text { Sample 2 } \
\hline \text { Sample size } & 8 & 13 \
\hline \text { Sample mean } & 80 & 115 \
\hline \text { Sample variance } & 450 & 100 \
\hline
\end{array}
\end{array}$$
A) -2.36
B) -0.22
C) -0.55
D) -4.38

Question

$$\begin{array}{l}
\text { In testing the equality of the two means below, what is the test statistic? (Use the unequal variances }\
\begin{array} { | l | c | c | } 
\hline & \text { Sample 1 } & \text { Sample 2 } \
\hline \text { Sample size } & 8 & 13 \
\hline \text { Sample mean } & 80 & 115 \
\hline \text { Sample variance } & 450 & 100 \
\hline
\end{array}
\end{array}$$
A) -2.36
B) -0.22
C) -0.55
D) -4.38

Quizplus · Accepted Answer

We need to use the t-test with unequal variances, which has the following formula for the test statistic:
$$t = \frac{\bar{X_1}-\bar{X_2}}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}$$
Plugging in the numbers from the table, we get:
$$t = \frac{80-115}{\sqrt{\frac{450}{8}+\frac{100}{13}}} \approx -4.38$$
Therefore, the test statistic is -4.38.

A) -236 B) -0

A) -236
B) -0