A researcher believes that the median annual rainfall in the valley is about $32.0$ inches. A randomly selected sample of 20 years had the following numbers of inches of rainfall in tl valley:
$$\begin{array} { l }
15.2,16.8,22.5,25.1,27.1,27.3,31.0,37.2,37.7,39.0,41.1,42.4,45.7,49.0,45 \
, 50.9,53.1,55.3,57.2,61.8
\end{array}$$
Test the researcher's hypothesis at $\alpha = 0.05$.
You may use the following abbreviated table of critical values for the sign test (two tailed $\alpha = 0.05$ ), taken from Table $J$ in the text:
$\begin{array}{l}
\begin{array}{l|cccccccc}
\mathbf{n} & 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 \
\hline \text { critical value } & 1 & 2 & 2 & 3 & 3 & 3 & 4 & 4
\end{array}\\
\begin{array}{l|ccccccc}
\mathbf{n} & \mathbf{1 9} & \mathbf{2 0} & \mathbf{2 1} & \mathbf{2 2} & \mathbf{2 3} & \mathbf{2 4} & \mathbf{2 5} \
\hline \text { critical value } & 4 & 5 & 5 & 5 & 6 & 6 & 6
\end{array}
\end{array}$
A) Accept, because the test value 7 is greater than the critical value 4.
B) Accept, because the test value 7 is greater than the critical value 5.
C) Reject, because the test value 6 is greater than the critical value 4.
D) Reject, because the test value 6 is greater than the critical value 5.

Question

A researcher believes that the median annual rainfall in the valley is about $32.0$ inches. A randomly selected sample of 20 years had the following numbers of inches of rainfall in tl valley:
$$\begin{array} { l } 
15.2,16.8,22.5,25.1,27.1,27.3,31.0,37.2,37.7,39.0,41.1,42.4,45.7,49.0,45 \
, 50.9,53.1,55.3,57.2,61.8
\end{array}$$
Test the researcher's hypothesis at $\alpha = 0.05$.
You may use the following abbreviated table of critical values for the sign test (two tailed $\alpha = 0.05$ ), taken from Table $J$ in the text:
$\begin{array}{l}
\begin{array}{l|cccccccc}
\mathbf{n} & 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 \
\hline \text { critical value } & 1 & 2 & 2 & 3 & 3 & 3 & 4 & 4
\end{array}\\
\begin{array}{l|ccccccc}
\mathbf{n} & \mathbf{1 9} & \mathbf{2 0} & \mathbf{2 1} & \mathbf{2 2} & \mathbf{2 3} & \mathbf{2 4} & \mathbf{2 5} \
\hline \text { critical value } & 4 & 5 & 5 & 5 & 6 & 6 & 6
\end{array}
\end{array}$
A) Accept, because the test value 7 is greater than the critical value 4.
B) Accept, because the test value 7 is greater than the critical value 5.
C) Reject, because the test value 6 is greater than the critical value 4.
D) Reject, because the test value 6 is greater than the critical value 5.

Quizplus · Accepted Answer

The Answer of A researcher believes that the median annual rainfall in the valley is about $32.0$ inches. A randomly selected sample of 20 years had the following numbers of inches of rainfall in tl valley:
$$\begin{array} { l } 
15.2,16.8,22.5,25.1,27.1,27.3,31.0,37.2,37.7,39.0,41.1,42.4,45.7,49.0,45 \
, 50.9,53.1,55.3,57.2,61.8
\end{array}$$
Test the researcher's hypothesis at $\alpha = 0.05$.
You may use the following abbreviated table of critical values for the sign test (two tailed $\alpha = 0.05$ ), taken from Table $J$ in the text:
$\begin{array}{l}
\begin{array}{l|cccccccc}
\mathbf{n} & 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 \
\hline \text { critical value } & 1 & 2 & 2 & 3 & 3 & 3 & 4 & 4
\end{array}\\
\begin{array}{l|ccccccc}
\mathbf{n} & \mathbf{1 9} & \mathbf{2 0} & \mathbf{2 1} & \mathbf{2 2} & \mathbf{2 3} & \mathbf{2 4} & \mathbf{2 5} \
\hline \text { critical value } & 4 & 5 & 5 & 5 & 6 & 6 & 6
\end{array}
\end{array}$
A) Accept, because the test value 7 is greater than the critical value 4.
B) Accept, because the test value 7 is greater than the critical value 5.
C) Reject, because the test value 6 is greater than the critical value 4.
D) Reject, because the test value 6 is greater than the critical value 5.

A Researcher Believes That the Median Annual Rainfall in the Valley