Assume that you want to test the claim that the paired sample data come from a population for which the mean difference
is $\mu _ { \mathrm { d } } = 0$ 0. Compute the value of the t test statistic. Round intermediate calculations to four decimal places as needed and
final answers to three decimal places as needed.
-The following table shows the weights of nine subjects before and after following a particular diet for two months. You wish to test the claim that the diet is effective in helping people lose weight. What is the value of
The appropriate test statistic? $\begin{array}{r|ccccccccc}
\text { Subject } & \text { A } & \text { B } & C & \text { D } & \text { E } & \text { F } & \text { G } & H & \text { I } \
\hline \text { Before } & 168 & 180 & 157 & 132 & 202 & 124 & 190 & 210 & 171 \
\hline \text { After } & 162 & 178 & 145 & 125 & 171 & 126 & 180 & 195 & 163
\end{array}$

A) $3.156$
B) $9.468$
C) $0.351$
D) $1.052$

Question

Assume that you want to test the claim that the paired sample data come from a population for which the mean difference
is $\mu _ { \mathrm { d } } = 0$ 0. Compute the value of the t test statistic. Round intermediate calculations to four decimal places as needed and
final answers to three decimal places as needed.
-The following table shows the weights of nine subjects before and after following a particular diet for two months. You wish to test the claim that the diet is effective in helping people lose weight. What is the value of
The appropriate test statistic? $\begin{array}{r|ccccccccc}
\text { Subject } & \text { A } & \text { B } & C & \text { D } & \text { E } & \text { F } & \text { G } & H & \text { I } \
\hline \text { Before } & 168 & 180 & 157 & 132 & 202 & 124 & 190 & 210 & 171 \
\hline \text { After } & 162 & 178 & 145 & 125 & 171 & 126 & 180 & 195 & 163
\end{array}$

A) $3.156$
B) $9.468$
C) $0.351$
D) $1.052$

Quizplus · Accepted Answer

We can use the paired sample t-test to test the null hypothesis that the mean difference in weight before and after the diet is zero.

The first step is to calculate the differences between before and after weights for each subject:

$\begin{array}{r|ccccccccc}
\text { Subject } & \text { A } & \text { B } & C & \text { D } & \text { E } & \text { F } & \text { G } & H & \text { I } \
\hline \text { Before } & 168 & 180 & 157 & 132 & 202 & 124 & 190 & 210 & 171 \
\hline \text { After } & 162 & 178 & 145 & 125 & 171 & 126 & 180 & 195 & 163 \
\hline \text { Difference } & -6 & -2 & -12 & -7 & -31 & 2 & -10 & -15 & -8
\end{array}$

The mean of these differences is:

$\overline{d} = \frac{\sum d_i}{n} = \frac{-79}{9} = -8.778$

The standard deviation of the differences is:

$s_d = \sqrt{\frac{\sum (d_i - \overline{d})^2}{n-1}} = \sqrt{\frac{742.556}{8}} = 8.602$

The t-test statistic is then:

$t = \frac{\overline{d} - \mu_d}{\frac{s_d}{\sqrt{n}}} = \frac{-8.778 - 0}{\frac{8.602}{\sqrt{9}}} = -3.156$

Using a t-distribution table with 8 degrees of freedom (n-1), we find that the p-value is less than 0.01. Therefore, we reject the null hypothesis and conclude that the diet is effective in helping people lose weight.

Assume That You Want to Test the Claim That the Paired