Question 1

A normal approximation for the Wilcoxon rank-sum test is appropriate when:

Accepted Answer

The answer of A normal approximation for the Wilcoxon rank-sum...

Question 2

The runs test is a nonparametric procedure for testing:

Accepted Answer

The runs test is used to test whether data are from a random process, meaning that there is no systematic pattern or trend in the data. It is a nonparametric test, meaning that it does not assume any specific distribution for the data. Therefore, the correct choice is (D). The runs test does not test for skewness or normality, nor does it test whether data are ordered.

Question 3

What is the nearest critical value for a Wilcoxon sign-ranked test with 15 nonzero differences, Ha:  , and α = 0.05?

Accepted Answer

The answer of What is the nearest critical value for...

Question 4

A normal approximation can be used in the Wilcoxon signed-rank test if:

Accepted Answer

The answer of A normal approximation can be used in...

Question 5

A manufacturer of ballpoint pens wishes to know if a machine designed to fill each individual pen with ink is operating properly.The median amount of ink should be 0.05 oz.Suppose 58 pens are randomly sampled from this particular machine, and none of the pens contains exactly 0.05 oz.Assuming the amount of ink in each pen is symmetrically distributed, conduct a Wilcoxon signed-rank test to see if the median amount of ink differs from 0.05 oz.The sum of positive differences (t+) from the sample is 502.Use a normal approximation and select the correct p-value and decision.(Use α = 0.05.)

Accepted Answer

Since the sample size is less than 30 and the distribution is assumed to be symmetric, we can use the Wilcoxon signed-rank test. The null and alternative hypotheses are:

H₀: The median amount of ink is 0.05 oz.
H₁: The median amount of ink is not 0.05 oz.

We need to calculate the test statistic W, which is the smaller of the sum of positive signed ranks and the sum of negative signed ranks. In this case, all the differences are positive, so W is equal to the sum of the ranks of the positive differences.

Since we have a sample size of 58, we can use a normal approximation to calculate the p-value. The test statistic is:

W = 502

The expected value of W under the null hypothesis is:

E(W) = n(n+1)/4 = 58*59/4 = 851

The standard deviation of W is:

SD(W) = sqrt(n*(n+1)*(2n+1)/24) = sqrt(58*59*117/24) = 67.8

The z-score is:

z = (502 - 851) / 67.8 = -4.86

Using a standard normal distribution table or calculator, the p-value is found to be approximately 0.0049. Since this p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that the median amount of ink differs from 0.05 oz. Therefore, the best choice is C.

Question 6

Researchers wish to test the effectiveness of a drug designed to treat depression.Seven clinically depressed patients are given a standardized depression test before taking the drug and are evaluated 4 weeks later using the same test.It is known that the scores from this particular test are not normally distributed.The scores are shown here. ​  ​
Use a sign test to conclude whether the drug can be associated with a median decrease in depression level.Choose the correct p-value and conclusion.(Use α = 0.05.)

Accepted Answer

The answer of Researchers wish to test the effectiveness of...

Question 7

A recent survey of practicing Jews, Christians, and Muslims asked these participants' their opinion concerning prayer in public schools.The possible responses were "Strongly For," "No Opinion," or "Strongly Against." The survey also asked several additional questions, which were used to create a continuous "religiosity" variable designed to indicate the amount of influence an individual's religion has on his or her daily life. ​  ​
Conduct a Kruskal-Wallis test to see if there is a significant difference in the religiosity of the response groups.Use a  approximation.Select the appropriate critical value (CV), test statistic (TS), and decision.(Use α = 0.01.)

Accepted Answer

The answer of A recent survey of practicing Jews, Christians,...

Question 8

Calculate the Spearman's rank correlation coefficient for the following data: ​  ​

Accepted Answer

The answer of Calculate the Spearman's rank correlation coefficient for...

Question 9

A runs test was performed on 200 measurements of beam deflections and resulted in a test statistic value of 2.486.Using a 5% significance level, what would you conclude about whether the sequence was produced in a random manner?

Accepted Answer

The test statistic value of 2.486 is greater than the critical value of 1.96 for a 5% significance level (two-tailed test), so we reject the null hypothesis and conclude that the sequence of observations is not random.

Question 10

In the Wilcoxon signed-rank test, if two or more measurements have the same nonzero difference, then:

Accepted Answer

When two or more measurements have the same nonzero difference, the scores are assigned the mean of the ranks of the tied values. This is known as the midrank method and is the most common method used in the Wilcoxon signed-rank test.

Question 11

Nonparametric tests can be appropriate for quantitative data when:

Accepted Answer

Nonparametric tests may be used when one or more of the assumptions underlying a particular parametric statistical test has been violated, such as when the data is not normally distributed or when the sample size is not sufficiently large. Nonparametric tests may help maintain statistical power and accuracy under such circumstances.

Question 12

Conduct a sign test on the following sample data to see if the median differs from 122. ​  ​
Choose the correct p-value and conclusion.(Use α = 0.10).

Accepted Answer

The answer of Conduct a sign test on the following...

Question 13

The Kruskal-Wallis test is the nonparametric version of the:

Accepted Answer

The Kruskal-Wallis test is a nonparametric test used to compare the median ranks of three or more independent groups. This makes it the nonparametric equivalent of the ANOVA F test, which is a parametric test used to compare the means of three or more independent groups. Therefore, the correct answer is B.

Question 14

If the underlying distributions are known to be symmetric, we can use the Wilcoxon rank-sum test to compare two independent population means.This is so because:

Accepted Answer

When the underlying distributions are known to be symmetric, the mean and the median have the same value for all symmetric distributions. Therefore, we can use the Wilcoxon rank-sum test to compare two independent population means, as it is designed to compare the medians of two samples.

Question 15

With the Wilcoxon sign-ranked test, what is done in the case of equal values?

Accepted Answer

In the Wilcoxon sign-ranked test, if equal values occur, they are assigned the mean rank for their positions in the ordered list. This ensures that the ranks assigned to the observations are fair and representative, and can help to preserve the integrity and reliability of the statistical analysis.

Question 16

A corporation wishes to evaluate the effectiveness of a new employee training program.Workers on two independent assembly lines are monitored, and the amount of time (in minutes) to complete a standardized assembly procedure is recorded for each.The distribution of assembly times is known to be heavily left-skewed.Based on the given sample information, does it appear that the training program is associated with a reduced median assembly time? Use the Wilcoxon rank-sum test to make your decision.Select the correct critical value (CV), test statistic (TS), and decision.(Use α = 0.05.) ​  ​

Accepted Answer

The answer of A corporation wishes to evaluate the effectiveness...

Question 17

An athletic trainer is concerned that his athletes are not drinking enough water during games.He randomly samples 11 previous games with comparable temperature and humidity and records the amount of water consumed by the team in liters (shown in the table).Conduct a sign test to see if the median amount of water consumed exceeds 30 L.(Assume that the amount of water consumed per game is a continuous variable.) ​
Amount of Water Consumed per Game (in liters)

Select the correct critical value (CV), test statistic (TS), and decision.(Use α = 0.10.)

Accepted Answer

To conduct a sign test: 
1. State the null hypothesis (H₀) and alternative hypothesis (H₁).
2. Determine the level of significance (α) and the critical value (CV).
3. Calculate the test statistic (TS).
4. Make a decision to either reject or fail to reject the null hypothesis.

Step 1: 
H₀: The median amount of water consumed is 30 L.
H₁: The median amount of water consumed is greater than 30 L.

Step 2: 
α = 0.10 (given). 
From the sign test table, the critical value for n = 11 with α = 0.10 is 8.

CV = 8

Step 3: 
To calculate the test statistic, we count the number of times the amount of water consumed was above 30 L. 
We have 8 positive signs and 3 negative signs.

TS = min(8, 3) = 3

Step 4: 
TS = 3 is less than CV = 8. Therefore, we fail to reject the null hypothesis. 
There is not enough evidence to conclude that the median amount of water consumed exceeds 30 L.

Question 18

Which of the following tests uses matched-pairs sampling?

Accepted Answer

The Wilcoxon signed-rank test uses matched-pairs sampling to compare the differences between two related groups.

Question 19

With the Kruskal-Wallis test, the data from all k samples are combined and each observation is assigned a rank.What is done in the case of equal values?

Accepted Answer

When there are ties (equal values), the mean rank is used for all tied observations. This approach ensures that the sum of the ranks equals the sum of the integers from 1 to N, where N is the total number of observations.

Question 20

Two variables have a Spearman's rank correlation coefficient of -0.9872.We can conclude from this that:

Accepted Answer

A Spearman's rank correlation coefficient of -0.9872 indicates a very strong negative correlation between the two variables. However, correlation does not imply causation, so we cannot conclude that there is a causal connection between the two variables. The two variables are clearly not uncorrelated (choice C), and we do not have any information about whether the samples are random (choice D).

Quiz 15: Nonparametric Statistics

A normal approximation for the Wilcoxon rank-sum test is appropriate when:

The runs test is a nonparametric procedure for testing:

What is the nearest critical value for a Wilcoxon sign-ranked test with 15 nonzero differences, Ha: , and α = 0.05?

A normal approximation can be used in the Wilcoxon signed-rank test if:

Calculate the Spearman's rank correlation coefficient for the following data:

A runs test was performed on 200 measurements of beam deflections and resulted in a test statistic value of 2.486.Using a 5% significance level, what would you conclude about whether the sequence was produced in a random manner?

In the Wilcoxon signed-rank test, if two or more measurements have the same nonzero difference, then:

Nonparametric tests can be appropriate for quantitative data when:

Conduct a sign test on the following sample data to see if the median differs from 122. Choose the correct p-value and conclusion.(Use α = 0.10) .

The Kruskal-Wallis test is the nonparametric version of the:

If the underlying distributions are known to be symmetric, we can use the Wilcoxon rank-sum test to compare two independent population means.This is so because:

With the Wilcoxon sign-ranked test, what is done in the case of equal values?

Which of the following tests uses matched-pairs sampling?

With the Kruskal-Wallis test, the data from all k samples are combined and each observation is assigned a rank.What is done in the case of equal values?

Two variables have a Spearman's rank correlation coefficient of -0.9872.We can conclude from this that:

Quiz 15: Nonparametric Statistics

A normal approximation for the Wilcoxon rank-sum test is appropriate when:

The runs test is a nonparametric procedure for testing:

What is the nearest critical value for a Wilcoxon sign-ranked test with 15 nonzero differences, Ha: , and α = 0.05?

A normal approximation can be used in the Wilcoxon signed-rank test if:

Calculate the Spearman's rank correlation coefficient for the following data: ​ ​

A runs test was performed on 200 measurements of beam deflections and resulted in a test statistic value of 2.486.Using a 5% significance level, what would you conclude about whether the sequence was produced in a random manner?

In the Wilcoxon signed-rank test, if two or more measurements have the same nonzero difference, then:

Nonparametric tests can be appropriate for quantitative data when:

Conduct a sign test on the following sample data to see if the median differs from 122. ​ ​ Choose the correct p-value and conclusion.(Use α = 0.10) .

The Kruskal-Wallis test is the nonparametric version of the:

If the underlying distributions are known to be symmetric, we can use the Wilcoxon rank-sum test to compare two independent population means.This is so because:

With the Wilcoxon sign-ranked test, what is done in the case of equal values?

Which of the following tests uses matched-pairs sampling?

With the Kruskal-Wallis test, the data from all k samples are combined and each observation is assigned a rank.What is done in the case of equal values?

Two variables have a Spearman's rank correlation coefficient of -0.9872.We can conclude from this that:

Calculate the Spearman's rank correlation coefficient for the following data:

Conduct a sign test on the following sample data to see if the median differs from 122. Choose the correct p-value and conclusion.(Use α = 0.10) .