It Is Believed That Children Can Throw a Ball Farther

Multiple Choice

It is believed that children can throw a ball farther after lunch than before lunch. A researcher decided to investigate this hypothesis for 14 children using the paired-sample sign test. Each of the distances below is in meters.
$\begin{array}{|c|c|c|}\hline \text { Subject } & \begin{array}{c}\text { Distance Before } \\\text { Lunch }\end{array} & \begin{array}{c}\text { Distance After } \\\text { Lunch }\end{array} \\\hline 1 & 27 & 31 \\\hline 2 & 31 & 39 \\\hline 3 & 29 & 37 \\\hline 4 & 28 & 24 \\\hline 5 & 31 & 39 \\\hline 6 & 41 & 37 \\\hline 7 & 16 & 20 \\\hline 8 & 27 & 31 \\\hline 9 & 29 & 37 \\\hline 10 & 54 & 66 \\\hline 11 & 16 & 20 \\\hline 12 & 41 & 37 \\\hline 13 & 28 & 24 \\\hline 14 & 29 & 37 \\\hline\end{array}$ At = .05, do the data support the claim? \[\begin{array}{l}
\text { You may use the following abbreviated table of critical values (one-tailed, } = .05 \text { ) taken from Table }\\
\(\begin{array}{|l|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline \mathrm{n} & 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 & 21 & 22 & 23 & 24 & 25 \\
\hline \text { critical value } & 2 & 2 & 3 & 3 & 3 & 4 & 4 & 5 & 5 & 5 & 6 & 6 & 7 & 7 & 7 \\
\hline
\end{array}\)

A) Supports the claim because the test value 4 is more than the critical value 3
B) Does not support the claim because the test value 4 is more than the critical value 3
C) Does not support the claim because the test value 4 is less than the critical value 8
D) Does not support the claim because the test value 4 is equal to the critical value 4