Question 1

Specify the rejection region for the Wilcoxon signed rank test in the following situation. $$n = 35 , \alpha = .10$$
$H _ { 0 }$ : Two probability distributions, 1 and 2, are identical
$H _ { \mathrm { a } }$ : Probability distribution of population 1 is shifted to the right or left of the probability distribution for population 2

Accepted Answer

The answer of Specify the rejection region for the Wilcoxon...

Question 2

A pharmaceutical company wishes to test a new drug with the expectation of lowering cholesterol levels. Ten subjects are randomly selected and their cholesterol levels are recorded. The results are listed below. The subjects were placed on the drug for a period of 6 months, after which their cholesterol levels were tested again. The results are listed below. (All units are milligrams per deciliter.) Use the Wilcoxon signed rank test to test the company's claim that the drug lowers cholesterol levels. Use $\alpha = .05$.
$\begin{array}{lcccccccccc}
\hline \text { Subject } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \
\hline \text { Before } & 217 & 249 & 226 & 257 & 183 & 187 & 259 & 196 & 199 & 182 \
\text { After } & 202 & 244 & 234 & 247 & 178 & 187 & 229 & 178 & 197 & 167
\end{array}$

Accepted Answer

The answer of A pharmaceutical company wishes to test a...

Question 3

A physician claims that a person's diastolic blood pressure can be lowered, if, instead of taking a drug, the person listens to a relaxation tape each evening. Ten subjects are randomly selected. Their blood pressures, measured in millimeters of mercury, are listed below. The 10 patients are given the tapes and told to listen to them each evening for one month. At the end of the month, their blood pressures are taken again. The data are listed below. Use the Wilcoxon signed rank test to test the physician's claim. Use $\alpha = .05$.
$\begin{array}{lcccccccccc}
\hline \text { Patient } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \
\hline \text { Before } & 86 & 91 & 87 & 82 & 99 & 90 & 96 & 89 & 92 & 84 \
\text { After } & 83 & 85 & 87 & 74 & 93 & 79 & 99 & 79 & 88 & 68
\end{array}$

Accepted Answer

The answer of A physician claims that a person's diastolic...

Question 4

Do popular diets really help customers in the long-run? Many diets help customers lose weight initially only to have the customer add the weight back on after the first few months on the diet. A
Commercially successful diet company conducted a study of twelve randomly selected customers
And measured their weight after before starting the diet and then again after staying with the diet
For a year. The company hoped that the initial weight loss would be sustained after the first year on
The diet. The data is shown below: $\begin{array}{c|c|c}
\text { Customer } & \text { Initial } & \text { One Year } \
\hline 1 & 185 & 175 \
2 & 192 & 193 \
3 & 125 & 115 \
4 & 148 & 146 \
5 & 165 & 170 \
6 & 220 & 175 \
7 & 265 & 170 \
8 & 177 & 174 \
9 & 302 & 266 \
10 & 112 & 116 \
11 & 154 & 148 \
12 & 230 & 256
\end{array}$

What alternative hypothesis should be tested in order to determine if the diet is successful at helping customers lose and keep weight off after one year?

A) The distribution of initial weight is shifted to the right or to the left of the distribution of one-year weight.
B) The distribution of initial weight is shifted to the right of the distribution of one-year weight.
C) The distribution of initial weight is identical to the distribution of one-year weight.
D) The distribution of initial weight is shifted to the left of the distribution of one-year weight.

Accepted Answer

The alternative hypothesis to test if the diet is successful at helping customers lose and keep weight off after one year is that the distribution of initial weight is shifted to the right of the distribution of one-year weight. This means that, on average, initial weights are higher than one-year weights, indicating weight loss.

Question 5

Do popular diets really help customers in the long-run? Many diets help customers lose weight initially only to have the customer add the weight back on after the first few months on the diet. A
Commercially successful diet company conducted a study of twelve randomly selected customers
And measured their weight after before starting the diet and then again after staying with the diet
For a year. The company hoped that the initial weight loss would be sustained after the first year on
The diet. The data is shown below: $\begin{array}{c|c|c}
\text { Customer } & \text { Initial } & \text { One Year } \
\hline 1 & 185 & 175 \
2 & 192 & 193 \
3 & 125 & 115 \
4 & 148 & 146 \
5 & 165 & 170 \
6 & 220 & 175 \
7 & 265 & 170 \
8 & 177 & 174 \
9 & 302 & 266 \
10 & 112 & 116 \
11 & 154 & 148 \
12 & 230 & 256
\end{array}$

Calculate the test statistic for the Wilcoxon Signed Rank Test to test to determine if the distribution of initial weight is shifted to the right of the distribution of one-year weight.
A) $\mathrm { T } _ { + } = 78$
B) $\mathrm { T } _ { + } = 59$
C) $\mathrm { T } _ { - } = 19$
D) $\mathrm { T } _ { + } = 26$

Accepted Answer

The answer of Do popular diets really help customers in...

Question 6

Nine students took the SAT test. Their scores are listed below. Later, they took a test preparation course and retook the SAT. Their new scores are listed below. Use the Wilcoxon signed rank test to test the claim that the test preparation had no effect on their scores. Use $\alpha = .05$.
$\begin{array}{lccccccccc}
\hline \text { Student } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \
\hline \text { Before Score } 950 & 1130 & 920 & 810 & 1160 & 830 & 840 & 970 & 870 \
\text { After Score } & 970 & 1130 & 910 & 850 & 1190 & 840 & 830 & 1010 & 890 \
\hline
\end{array}$

Accepted Answer

The answer of Nine students took the SAT test. Their...

Question 7

A weight-lifting coach claims that a weight-lifter can increase strength by taking vitamin E. To test the theory, the coach randomly selects 9 athletes and gives them a strength test using a bench press. The results are listed below. Thirty days later, after regular training supplemented by vitamin E, they are tested again. The new results are listed below. Use the Wilcoxon signed rank test to find the critical value to test the claim that the vitamin $\mathrm { E }$ supplement is effective in increasing the athletes' strength. Use $\alpha = .05$.
$\begin{array}{lccccccccc}
\hline \text { Athlete } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \
\hline \text { before } & 204 & 274 & 264 & 206 & 270 & 219 & 226 & 196 & 267 \
\text { After } & 214 & 279 & 264 & 204 & 277 & 234 & 231 & 191 & 272
\end{array}$

Accepted Answer

The answer of A weight-lifting coach claims that a weight-lifter...

Question 8

When performing a signed rank test in a paired difference experiment, tied absolute value
differences are assigned the average of the ranks they would receive if they were unequal, but
successive measurements.

Accepted Answer

In a signed rank test, when there are tied absolute value differences, the procedure is to assign the average of the ranks that these tied values would have received if they were not tied. This ensures that the ranking is fair and maintains the integrity of the test's assumptions.

Question 9

A scientist is hoping to compare the levels of DDT toxin found in three species of fish in a local river. He randomly samples 7 of each species to use in the analysis. For each fish, he measures the
Amount of DDT toxin present. The data is shown below:

Ideally he will be able to determine if a difference exists in the population of DDT toxins found in the three fish species. Identify the test statistic for the Kruskal-Wallis H-Test.
A) $\mathrm { H } = 10.286$
B) $\mathrm { H } = 17.0$
C) $\mathrm { H } = 11.718$
D) $\mathrm { H } = 5.714$

Accepted Answer

The answer of A scientist is hoping to compare the...

Question 10

A local school district is concerned about the number of school days missed by its teachers due to illness. A random sample of 10 teachers is selected. The numbers of days absent in one year is listed below. An incentive program is offered in an attempt to decrease the number of days absent.The number of days absent in one year after the incentive program is listed below. Use the Wilcoxon signed rank test to test the claim that the incentive program cuts down on the number of days missed by teachers. Use $\alpha = .05$.
$\begin{array}{lcccccccccc}
\hline \text { Teacher } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \
\hline \text { Days Absent } & & & & & & & & & & \
\text { Before Incentive } & 8 & 6 & 7 & 3 & 9 & 6 & 2 & 7 & 9 & 4 \
\text { Days Absent } & & & & & & & & & & \
\text { After Incentive } & 6 & 5 & 7 & 1 & 8 & 4 & 0 & 8 & 7 & 4
\end{array}$

Accepted Answer

The answer of A local school district is concerned about...

Question 11

For a valid signed rank test, the probability distribution from which the sample of paired
differences is drawn must be continuous.

Accepted Answer

The Wilcoxon signed-rank test assumes that the differences between pairs are drawn from a continuous distribution to accurately rank the differences and calculate the test statistic.

Question 12

When applying the Wilcoxon signed rank test, the number of ties should be small relative to the
number of observations to ensure the validity of the test.

Accepted Answer

The Wilcoxon signed rank test assumes that ties (observations with the same value) are rare. A large number of ties can affect the distribution of the test statistic, potentially leading to inaccurate results.

Question 13

For a valid Kruskal-Wallis test, the probability distribution from which the samples are drawn
must be continuous.

Accepted Answer

The Kruskal-Wallis test assumes that the samples come from a continuous distribution, as it ranks the data across all groups.

Question 14

A scientist is hoping to compare the levels of DDT toxin found in three species of fish in a local river. He randomly samples 50 of each species to use in the analysis. For each fish, he measures the
Amount of DDT toxin present. Ideally he will be able to determine if a difference exists in the
Population of DDT toxins found in the three fish species. What type of nonparametric analysis
Should be used? 
A) The Wilcoxon Rank Sum Test
B) The Friedman $\mathrm { F } _ { \mathbf { r } }$-Test
C) The Wilcoxon Signed Rank Test
D) The Kruskal-Wallis H-Test
E) The Sign Test

Accepted Answer

The Kruskal-Wallis H-Test is the correct nonparametric analysis for comparing the levels of a variable (in this case, DDT toxin) across three or more independent groups (the three species of fish). This test does not assume a normal distribution of the data, making it suitable for nonparametric data analysis.

Question 15

Do popular diets really help customers in the long-run? Many diets help customers lose weight initially only to have the customer add the weight back on after the first few months on the diet. A
Commercially successful diet company conducted a study of twelve randomly selected customers
And measured their weight after before starting the diet and then again after staying with the diet
For a year. The company hoped that the initial weight loss would be sustained after the first year on
The diet. The data is shown below: $\begin{array}{c|c|c}
\text { Customer } & \text { Initial } & \text { One Year } \
\hline 1 & 185 & 175 \
2 & 192 & 193 \
3 & 125 & 115 \
4 & 148 & 146 \
5 & 165 & 170 \
6 & 220 & 175 \
7 & 265 & 170 \
8 & 177 & 174 \
9 & 302 & 266 \
10 & 112 & 116 \
11 & 154 & 148 \
12 & 230 & 256
\end{array}$

Find the rejection region for the Wilcoxon Signed Rank Test to test to determine if the distribution of initial weight is shifted to the right of the distribution of one-year weight. Test using $\alpha = 0.05$.
A) $T _ { - } \leq 14$
B) $\mathrm { T } _ { - } \leq 7$
C) $\mathrm { T } _ { - } \leq 10$
D) $T _ { - } \leq 17$

Accepted Answer

The answer of Do popular diets really help customers in...

Question 16

In a study of the effectiveness of physical exercise on weight loss, 20 people were randomly selected to participate in a program for 30 days. Use the Wilcoxon signed rank test to test the claim that exercise has no bearing on weight loss. Use $\alpha = .02$.

Accepted Answer

The answer of In a study of the effectiveness of...

Question 17

Specify the rejection region for the Wilcoxon signed rank test in the following situation. $$n = 25 , \alpha = .05$$
$H _ { 0 }$ : Two probability distributions, 1 and 2, are identical
$H _ { \mathrm { a } }$ : Probability distribution of population 1 is shifted to the right of the probability distribution for population 2

Accepted Answer

The answer of Specify the rejection region for the Wilcoxon...

Question 18

A certain manufacturer is interested in evaluating two alternative manufacturing plans consisting of different machine layouts. Because of union rules, hours of operation vary greatly for this
Particular manufacturer from one day to the next. Twenty-eight random working days were
Selected and each plan was monitored and the number of items produced each day was recorded.
Some of the collected data is shown below:

It was desired to test to determine if the distribution of output for plan 2 was shifted to the right of the distribution of output for plan 1 . What type of nonparametric analysis should be used?
A) The Wilcoxon Rank Sum Test
B) The Sign Test
C) The Kruskal-Wallis H-Test
D) The Friedman $\mathrm { F } _ { \mathrm { r } }$-Test
E) The Wilcoxon Signed Rank Test

Accepted Answer

The answer of A certain manufacturer is interested in evaluating...

Question 19

The Kruskal-Wallis test is valid only when each sample contains five or fewer measurements.

Accepted Answer

The Kruskal-Wallis test does not have a strict requirement for each sample to contain five or fewer measurements. It is a non-parametric method for testing whether samples originate from the same distribution and can be used for samples of virtually any size, assuming other assumptions of the test are met.

Question 20

The Wilcoxon signed rank test for large samples can be used when n ≥ 10.

Accepted Answer

The Wilcoxon signed rank test for large samples is typically used when the sample size n is greater than or equal to 30, not 10.

Quiz 14: Nonparametric Statistics Available Online

When performing a signed rank test in a paired difference experiment, tied absolute value differences are assigned the average of the ranks they would receive if they were unequal, but successive measurements.

For a valid signed rank test, the probability distribution from which the sample of paired differences is drawn must be continuous.

When applying the Wilcoxon signed rank test, the number of ties should be small relative to the number of observations to ensure the validity of the test.

For a valid Kruskal-Wallis test, the probability distribution from which the samples are drawn must be continuous.

In a study of the effectiveness of physical exercise on weight loss, 20 people were randomly selected to participate in a program for 30 days. Use the Wilcoxon signed rank test to test the claim that exercise has no bearing on weight loss. Use α=.02\alpha = .02α=.02 .

The Kruskal-Wallis test is valid only when each sample contains five or fewer measurements.

The Wilcoxon signed rank test for large samples can be used when n ≥ 10.