In a test of the difference between the two means below, what should the test value be for a $t$ test?
$\begin{array}{lcc}
\hline & \text { Sample 1 } & \text { Sample 2 } \
\hline \text { Sample mean } & 680 & 735 \
\text { Sample variance } & 550 & 60 \
\text { Sample size } & 10 & 11
\end{array}$

A) -0.31
B) -0.91
C) -7.07
D) -0.11

Question

In a test of the difference between the two means below, what should the test value be for a $t$ test?
$\begin{array}{lcc}
\hline & \text { Sample 1 } & \text { Sample 2 } \
\hline \text { Sample mean } & 680 & 735 \
\text { Sample variance } & 550 & 60 \
\text { Sample size } & 10 & 11
\end{array}$

A) -0.31
B) -0.91
C) -7.07
D) -0.11

Quizplus · Accepted Answer

The test value for a $t$ test comparing two means can be calculated using the formula: $$t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}$$ where $\bar{x}_1$ and $\bar{x}_2$ are the sample means, $s_1^2$ and $s_2^2$ are the sample variances, and $n_1$ and $n_2$ are the sample sizes for the two samples, respectively. Plugging in the given values: $$t = \frac{680 - 735}{\sqrt{\frac{550}{10} + \frac{60}{11}}} = \frac{-55}{\sqrt{55 + \frac{60}{11}}} = \frac{-55}{\sqrt{55 + 5.45}} = \frac{-55}{\sqrt{60.45}} \approx -7.07.$$ This calculation shows that the correct test value is approximately -7.07, which corresponds to choice C.

In a Test of the Difference Between the Two Means ttt

In a Test of the Difference Between the Two Means $t$