A cholesterol test was given to 10 heart patients with high cholesterol levels.The same 10 heart patients are then given a new cholesterol-reducing drug for six months.Before the patients begin taking the drug,they are told to maintain their current diets and eating habits so that the effect of the drug can be more effectively determined.After taking the drug for six months,the same patients are given a cholesterol test again.The cholesterol levels before and after taking the drug are given below.The cholesterol level readings are not normally distributed.At ? = .05,test to determine if the drug is helpful in reducing cholesterol levels. $$\begin{array} { c c c }
& { \text { Cholesterol level } } \
\text { Patient } & \text { Before } & \text { After } \
1 & 210 & 205 \
2 & 208 & 204 \
3 & 185 & 186 \
4 & 215 & 207 \
5 & 192 & 193 \
6 & 218 & 214 \
7 & 170 & 178 \
8 & 196 & 190 \
9 & 220 & 212 \
10 & 215 & 204
\end{array}$$
)
A)Reject the null hypothesis.
B)Do not reject the null hypothesis.
Reject $\mathrm { H } _ { 0 }$ if $T _ { - } \leq T _ { 0510 }$
$$T _ { .05,10 } = 11$$
$$\begin{array} { c c c c c c c }
& \text { Cholesterol level } & & & & \
\text { Patient } & \text { Before } & \text { After } & \left( d _ { i } \right) & \left| d _ { i } \right| & \text { Ranks } & \text { Neg.Ranks } \
1 & 210 & 205 & 5 & 5 & 5 & \
2 & 208 & 204 & 4 & 4 & 3.5 & \
3 & 185 & 186 & - 1 & 1 & 1.5 & 1.5 \
4 & 215 & 207 & 8 & 8 & 8 & \
5 & 192 & 193 & - 1 & 1 & 1.5 & 1.5 \
6 & 218 & 214 & 4 & 4 & 3.5 & \
7 & 170 & 178 & - 8 & 8 & 8 & 8 \
8 & 196 & 190 & 6 & 6 & 6 & \
9 & 220 & 212 & 8 & 8 & 8 & \
10 & 215 & 204 & 11 & 11 & 10 &
\end{array}$$

Question

A cholesterol test was given to 10 heart patients with high cholesterol levels.The same 10 heart patients are then given a new cholesterol-reducing drug for six months.Before the patients begin taking the drug,they are told to maintain their current diets and eating habits so that the effect of the drug can be more effectively determined.After taking the drug for six months,the same patients are given a cholesterol test again.The cholesterol levels before and after taking the drug are given below.The cholesterol level readings are not normally distributed.At ? = .05,test to determine if the drug is helpful in reducing cholesterol levels. $$\begin{array} { c c c } 
& { \text { Cholesterol level } } \
\text { Patient } & \text { Before } & \text { After } \
1 & 210 & 205 \
2 & 208 & 204 \
3 & 185 & 186 \
4 & 215 & 207 \
5 & 192 & 193 \
6 & 218 & 214 \
7 & 170 & 178 \
8 & 196 & 190 \
9 & 220 & 212 \
10 & 215 & 204
\end{array}$$
)
A)Reject the null hypothesis.
B)Do not reject the null hypothesis.
Reject $\mathrm { H } _ { 0 }$ if $T _ { - } \leq T _ { 0510 }$
$$T _ { .05,10 } = 11$$
$$\begin{array} { c c c c c c c } 
& \text { Cholesterol level } & & & & \
\text { Patient } & \text { Before } & \text { After } & \left( d _ { i } \right) & \left| d _ { i } \right| & \text { Ranks } & \text { Neg.Ranks } \
1 & 210 & 205 & 5 & 5 & 5 & \
2 & 208 & 204 & 4 & 4 & 3.5 & \
3 & 185 & 186 & - 1 & 1 & 1.5 & 1.5 \
4 & 215 & 207 & 8 & 8 & 8 & \
5 & 192 & 193 & - 1 & 1 & 1.5 & 1.5 \
6 & 218 & 214 & 4 & 4 & 3.5 & \
7 & 170 & 178 & - 8 & 8 & 8 & 8 \
8 & 196 & 190 & 6 & 6 & 6 & \
9 & 220 & 212 & 8 & 8 & 8 & \
10 & 215 & 204 & 11 & 11 & 10 &
\end{array}$$

Quizplus · Accepted Answer

We need to calculate the Wilcoxon signed-rank test statistic, which is the smaller of the sum of positive ranks and the sum of negative ranks. Here, the sum of positive ranks is 37.5 and the sum of negative ranks is 4.5. Therefore, the test statistic is 4.5. Since there are 10 patients, the critical value at α = .05 and two-tailed test is 11. Since the test statistic is less than the critical value, we do not have enough evidence to reject the null hypothesis. However, if we look at the data, we can see that 7 out of 10 patients have lower cholesterol levels after taking the drug, which suggests that the drug may be helpful in reducing cholesterol levels.

A Cholesterol Test Was Given to 10 Heart Patients with High