A study was conducted to investigate the effect of an intervention protocol on IQ tests.Nine randomly selected students were tested. $$\begin{array} { l c }
\text { Before } & \text { After } \
100 & 106 \
111 & 112 \
93 & 95 \
92 & 90 \
99 & 107 \
85 & 100 \
117 & 126 \
110 & 105 \
98 & 110
\end{array}$$
At ? = .05,test to determine if the protocol increases test scores.
A)Reject the null hypothesis.
B)Fail to reject the null hypothesis.
$\begin{array}{c}
\begin{array}{l}
\underline{\text { Before }}\
100 \
111 \
93 \
92 \
99 \
85 \
117 \
110 \
98
\end{array}
\begin{array}{c}
\underline{\text { After }} \
106 \
112 \
95 \
90 \
107 \
100 \
126 \
105 \
110
\end{array}
\begin{array}{c}
\underline{d}\
-6 \
-1 \
-2 \
2 \
-8 \
-15 \
-9 \
5 \
-12 \
\end{array}
\begin{array}{c}
\underline{ |d|}\
6 \
1 \
2 \
2 \
8 \
15 \
9 \
5 \
12
\end{array}
\begin{array}{c}
\underline{\text { Rank }} \
5 \
1 \
2.5 \
2.5 \
6 \
9 \
7 \
4 \
8
\end{array}

\end{array}$

Question

A study was conducted to investigate the effect of an intervention protocol on IQ tests.Nine randomly selected students were tested. $$\begin{array} { l c } 
\text { Before } & \text { After } \
100 & 106 \
111 & 112 \
93 & 95 \
92 & 90 \
99 & 107 \
85 & 100 \
117 & 126 \
110 & 105 \
98 & 110
\end{array}$$
At ? = .05,test to determine if the protocol increases test scores.
A)Reject the null hypothesis.
B)Fail to reject the null hypothesis.
$\begin{array}{c}
\begin{array}{l}
\underline{\text { Before }}\
100 \
111 \
93 \
92 \
99 \
85 \
117 \
110 \
98 
\end{array}
\begin{array}{c}
\underline{\text { After }} \
106 \
112 \
95 \
90 \
107 \
100 \
126 \
105 \
110 
\end{array}
\begin{array}{c}
\underline{d}\
-6 \
-1 \
-2 \
2 \
-8 \
-15 \
-9 \
5 \
-12 \
\end{array}
\begin{array}{c}
\underline{ |d|}\
6 \
1 \
2 \
2 \
8 \
15 \
9 \
5 \
12
\end{array}
\begin{array}{c}
\underline{\text { Rank }} \
 5 \
1 \
2.5 \
2.5 \
6 \
9 \
7 \
4 \
8 
\end{array}

\end{array}$

Quizplus · Accepted Answer

We need to perform a Wilcoxon signed-rank test to determine if the intervention protocol has a significant effect on IQ test scores. The null hypothesis is that there is no difference between the before and after scores, and the alternative hypothesis is that the intervention protocol increases test scores.

Using a significance level of α = 0.05, we look up the appropriate critical value in the Wilcoxon signed-rank table (or use a software package). For a sample size of n=9, the critical value is 6.

Next, we calculate the signed ranks of the differences between the before and after scores. We also calculate the absolute values of these differences and rank them.

The total of the positive ranks is 23, and the total of the negative ranks is 12. We take the smaller of these values as our test statistic, which is 12.

Since 12 is less than the critical value of 6, we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the intervention protocol increases IQ test scores.

A Study Was Conducted to Investigate the Effect of an Intervention