Question 1

The Wilcoxon rank-sum test is an appropriate test when:

Accepted Answer

A)  comparing two population proportions, assuming the underlying distributions are normal. 
B)  comparing two population medians, assuming both populations are mound-shaped symmetric. 
C)  comparing two population medians when the underlying distributions are non-normal or when the data are ranks. 
D)  testing whether the median value from a single population is different from an assumed value when the distribution is normal. 
A)  comparing two population proportions, assuming the underlying distributions are normal. 
B)  comparing two population medians, assuming both populations are mound-shaped symmetric. 
C)  comparing two population medians when the underlying distributions are non-normal or when the data are ranks. 
D)  testing whether the median value from a single population is different from an assumed value when the distribution is normal.

Question 2

Which of the following tests uses matched-pairs sampling?

Accepted Answer

A)  Wilcoxon signed-rank test 
B)  Wilcoxon rank-sum test 
C)  Mann-Whitney test 
D)  Kruskal-Wallis test 
A)  Wilcoxon signed-rank test 
B)  Wilcoxon rank-sum test 
C)  Mann-Whitney test 
D)  Kruskal-Wallis test

Question 3

A study looked at x = distance of convenience stores from a large city's Contemporary Art Museum, and y = price of a 50-mL bottle of water at the stores.The Spearman's rank correlation coefficient was calculated to be -0.73.What does this tell you about the variables?

Accepted Answer

A)  There is no association between distance from the museum and the price of bottled water. 
B)  There is an association between these variables: On average, the farther a convenience store is from the museum, the less expensive a bottle of water is at the store. 
C)  There is an association between these variables: On average, the farther a convenience store is from the museum, the more expensive a bottle of water is at the store. 
D)  The distance of a convenience store from the museum determines the price of a bottle of water at the store. 
A)  There is no association between distance from the museum and the price of bottled water. 
B)  There is an association between these variables: On average, the farther a convenience store is from the museum, the less expensive a bottle of water is at the store. 
C)  There is an association between these variables: On average, the farther a convenience store is from the museum, the more expensive a bottle of water is at the store. 
D)  The distance of a convenience store from the museum determines the price of a bottle of water at the store.

Question 4

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

Accepted Answer

A)  t test on two proportions. 
B)  ANOVA F test. 
C)  multiple regression t test for a significant predictor. 
D)  paired t test. 
A)  t test on two proportions. 
B)  ANOVA F test. 
C)  multiple regression t test for a significant predictor. 
D)  paired t test.

Question 5

Which of the following is a disadvantage of the sign test?

Accepted Answer

A)  Tied pairs are not considered in the analysis. 
B)  Only the signs of the differences, not the actual values, are used in the analysis. 
C)  The sign test cannot be used when the sample sizes are small. 
D)  The results from a sign test have little practical value. 
A)  Tied pairs are not considered in the analysis. 
B)  Only the signs of the differences, not the actual values, are used in the analysis. 
C)  The sign test cannot be used when the sample sizes are small. 
D)  The results from a sign test have little practical value.

Question 6

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

Accepted Answer

A)    . 
B)    . 
C)    . 
D)    for all categories. 
A)    . 
B)    . 
C)    . 
D)    for all categories.

Question 7

When performing a Wilcoxon rank-sum test on the two independent samples shown here at α = 0.01, what is the alternative hypothesis? ​   .

Accepted Answer

A)  The samples have statistically different means. 
B)  The samples have the same median. 
C)  The samples have statistically different medians. 
D)  The samples have the same mean. 
A)  The samples have statistically different means. 
B)  The samples have the same median. 
C)  The samples have statistically different medians. 
D)  The samples have the same mean.

Question 8

Suppose a pair of dice is rolled 50 times to determine if "doubles" occur randomly.The following results were obtained (N = not a double, Y = double): N N Y N Y Y N N N N N N Y N Y N N N N N N Y N N N N N N Y N Y N N Y N N N N N Y N N N N N N N N N N
How many runs are there in these data?

Accepted Answer

A)  10 
B)  17 
C)  19 
D)  40 
A)  10 
B)  17 
C)  19 
D)  40

Question 9

A meteorologist has measured the amount of rain in four cities for the last six months.She wants to know if there are different amounts of rain in the four cities.The table shows the data. ​   ​
Conduct a Kruskal-Wallis test to see if there is a significant difference in the amount of rain in the four cities.Use a χ2 approximation.Select the appropriate critical value (CV), test statistic (TS), and decision.(Use α = 0.025.)

Accepted Answer

A)  CV = 7.3778, TS = 14.04, reject H₀ 
B)  CV = 9.2103, TS = 15.98, reject H₀ 
C)  CV = 9.3484, TS = 15.98, reject H₀ 
D)  CV = 9.3484, TS = 9.22, fail to reject H₀ 
A)  CV = 7.3778, TS = 14.04, reject H₀ 
B)  CV = 9.2103, TS = 15.98, reject H₀ 
C)  CV = 9.3484, TS = 15.98, reject H₀ 
D)  CV = 9.3484, TS = 9.22, fail to reject H₀

Question 10

In the sign test on a population median, what is done with values equal to the hypothesized median?

Accepted Answer

A)  Every other one is given a positive sign. 
B)  They are excluded from the analysis. 
C)  They are all averaged, and if the average is greater than the median a positive sign is assigned to them. 
D)  In a continuous distribution, the probability of a value being exactly equal to the median is zero, so this will never occur. 
A)  Every other one is given a positive sign. 
B)  They are excluded from the analysis. 
C)  They are all averaged, and if the average is greater than the median a positive sign is assigned to them. 
D)  In a continuous distribution, the probability of a value being exactly equal to the median is zero, so this will never occur.

Question 11

Concerning the Kruskal-Wallis test, the test statistic follows a chi-square distribution with   degrees of freedom if H₀ is true and:

Accepted Answer

A)    . 
B)    . 
C)    . 
D)    .and   
A)    . 
B)    . 
C)    . 
D)    .and

Question 12

The first 10 final exams turned in for a particular class are classified as either pass (earned a grade of "C" or higher) or fail (earned a grade lower than "C").The sequence of exam submission and the results are shown here: ​   ​
Use the runs test with α = 0.05 to determine whether there is any evidence that the order in which the exams were submitted was not random.Select the appropriate critical values (CV), test statistic (TS), and decision.

Accepted Answer

A)  CV = 3 and 9, TS = 5, fail to reject H₀ 
B)  CV = 3 and 8, TS = 5, fail to reject H₀ 
C)  CV = 3 and 9, TS = 3, reject H₀ 
D)  CV = 2 and 8, TS = 2, reject H₀ 
A)  CV = 3 and 9, TS = 5, fail to reject H₀ 
B)  CV = 3 and 8, TS = 5, fail to reject H₀ 
C)  CV = 3 and 9, TS = 3, reject H₀ 
D)  CV = 2 and 8, TS = 2, reject H₀

Question 13

A two-sample t test with independent samples is the parametric version of a:

Accepted Answer

A)  Wilcoxon signed-rank test for paired samples. 
B)  Wilcoxon rank-sum test. 
C)  Wilcoxon signed-rank test for one sample. 
D)  runs test. 
A)  Wilcoxon signed-rank test for paired samples. 
B)  Wilcoxon rank-sum test. 
C)  Wilcoxon signed-rank test for one sample. 
D)  runs test.

Question 14

Maintenance is done to increase the printing speed of an office printer.The amount of time (in seconds) for each of the six employees to print a standardized report using this printer before the maintenance is recorded in the table.The amount of time for the same employees to print these same reports after the maintenance is also recorded. ​   ​
Assuming the distributions are symmetric and continuous, conduct a Wilcoxon signed-rank test to see if it appears that the median print time decreased after the maintenance.Select the correct critical value (CV), test statistic (TS), and decision.(Use α = 0.10.)

Accepted Answer

A)  CV = 6, TS = 18, reject H₀ 
B)  CV = 17, TS = 14, fail to reject H₀ 
C)  CV = 2, TS = 10, reject H₀ 
D)  CV = 13, TS = 14, reject H₀ 
A)  CV = 6, TS = 18, reject H₀ 
B)  CV = 17, TS = 14, fail to reject H₀ 
C)  CV = 2, TS = 10, reject H₀ 
D)  CV = 13, TS = 14, reject H₀

Question 15

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

A)  p = 0.0592; there is sufficient statistical evidence to reject the null hypothesis and state that the median appears to be different than 122. 
B)  p = 0.3018; there is insufficient evidence to state that the median differs from 122. 
C)  p = 0.1509; there is sufficient statistical evidence to reject the null hypothesis and state that the median appears to be different than 122. 
D)  p = 0.8491; there is insufficient evidence to reject the null hypothesis and state that the median differs from 122. 
A)  p = 0.0592; there is sufficient statistical evidence to reject the null hypothesis and state that the median appears to be different than 122. 
B)  p = 0.3018; there is insufficient evidence to state that the median differs from 122. 
C)  p = 0.1509; there is sufficient statistical evidence to reject the null hypothesis and state that the median appears to be different than 122. 
D)  p = 0.8491; there is insufficient evidence to reject the null hypothesis and state that the median differs from 122.

Question 16

The amount of time spent waiting for the bus at a city bus stop is symmetrically distributed.Eight randomly sampled people who catch the bus at this stop are asked how long they had to wait.Their wait times (in minutes) are: ​   ​
Conduct a Wilcoxon signed-rank test to see if the median wait time is more than 20 minutes.Select the correct critical value (CV), test statistic (TS), and decision.(Use α = 0.05.)

Accepted Answer

A)  CV = 6, TS = 4, reject H₀ 
B)  CV = 30, TS = 4, fail to reject H₀ 
C)  CV = 30, TS = 3, reject H₀ 
D)  CV = 6, TS = 4, fail to reject H₀ 
A)  CV = 6, TS = 4, reject H₀ 
B)  CV = 30, TS = 4, fail to reject H₀ 
C)  CV = 30, TS = 3, reject H₀ 
D)  CV = 6, TS = 4, fail to reject H₀

Question 17

As used in the runs test, a run is:

Accepted Answer

A)  a series, or subsequence, of one or more identical observations. 
B)  a series, or subsequence, of two or more identical observations. 
C)  a series, or subsequence, of one or more unusual observations. 
D)  a series, or subsequence, of two or more unusual observations. 
A)  a series, or subsequence, of one or more identical observations. 
B)  a series, or subsequence, of two or more identical observations. 
C)  a series, or subsequence, of one or more unusual observations. 
D)  a series, or subsequence, of two or more unusual observations.

Question 18

The first 10 final exams turned in for a particular class are classified as either pass (earned a grade of "C" or higher) or fail (earned a grade lower than "C").The sequence of exam submission and the results are shown here: ​   ​
A runs test with α = 0.05 is used to determine whether there is any evidence that the order in which the exams were submitted was not random.What is the alternative hypothesis in this case?

Accepted Answer

A)  The statistics will conform that the distribution is random. 
B)  The distribution can be modeled as a normal curve. 
C)  There is not alternative hypothesis; there are too few data points to analyze correctly. 
D)  The distribution is not random. 
A)  The statistics will conform that the distribution is random. 
B)  The distribution can be modeled as a normal curve. 
C)  There is not alternative hypothesis; there are too few data points to analyze correctly. 
D)  The distribution is not random.

Question 19

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

A) 2.486 > 1.96, so reject the null hypothesis and conclude the sequence of observations is not random. B) 2.4868 > 1.96, so do not reject the null hypothesis and conclude the sequence of observations may well be random. C) 2.486 < 2.575, so reject the null hypothesis and conclude the sequence of observations is not random. D) 2.486 < 2.575, so do not reject the null hypothesis and conclude the sequence of observations may well be random. A) 2.486 > 1.96, so reject the null hypothesis and conclude the sequence of observations is not random. B) 2.4868 > 1.96, so do not reject the null hypothesis and conclude the sequence of observations may well be random. C) 2.486 < 2.575, so reject the null hypothesis and conclude the sequence of observations is not random. D) 2.486 < 2.575, so do not reject the null hypothesis and conclude the sequence of observations may well be random.

Question 20

Calculate the Spearman's rank correlation coefficient for the following rankings by x and y: ​   ​

Accepted Answer

A)  0.30 
B)  0.70 
C)  0.75 
D)  1.00 
A)  0.30 
B)  0.70 
C)  0.75 
D)  1.00

The Wilcoxon rank-sum test is an appropriate test when:

Which of the following tests uses matched-pairs sampling?

A study looked at x = distance of convenience stores from a large city's Contemporary Art Museum, and y = price of a 50-mL bottle of water at the stores.The Spearman's rank correlation coefficient was calculated to be -0.73.What does this tell you about the variables?

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

Which of the following is a disadvantage of the sign test?

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

When performing a Wilcoxon rank-sum test on the two independent samples shown here at α = 0.01, what is the alternative hypothesis? .

Suppose a pair of dice is rolled 50 times to determine if "doubles" occur randomly.The following results were obtained (N = not a double, Y = double): N N Y N Y Y N N N N N N Y N Y N N N N N N Y N N N N N N Y N Y N N Y N N N N N Y N N N N N N N N N N How many runs are there in these data?

In the sign test on a population median, what is done with values equal to the hypothesized median?

Concerning the Kruskal-Wallis test, the test statistic follows a chi-square distribution with degrees of freedom if H₀ is true and:

A two-sample t test with independent samples is the parametric version of a:

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).

As used in the runs test, a run is:

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?

Calculate the Spearman's rank correlation coefficient for the following rankings by x and y:

Why Study Statistics

An Introduction to Statistics and Statistical Inference

Tables and Graphs for Summarizing Data

Numerical Summary Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Confidence Intervals Based on a Single Sample

Hypothesis Tests Based on a Single Sample

Confidence Intervals and Hypothesis Tests Based on Two Samples or Treatments

The Analysis of Variance

Correlation and Linear Regression

Categorical Data and Frequency Tables

Filters

Exam 15: Nonparametric Statistics

The Wilcoxon rank-sum test is an appropriate test when:

Which of the following tests uses matched-pairs sampling?

A study looked at x = distance of convenience stores from a large city's Contemporary Art Museum, and y = price of a 50-mL bottle of water at the stores.The Spearman's rank correlation coefficient was calculated to be -0.73.What does this tell you about the variables?

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

Which of the following is a disadvantage of the sign test?

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

When performing a Wilcoxon rank-sum test on the two independent samples shown here at α = 0.01, what is the alternative hypothesis? ​ .

Suppose a pair of dice is rolled 50 times to determine if "doubles" occur randomly.The following results were obtained (N = not a double, Y = double): N N Y N Y Y N N N N N N Y N Y N N N N N N Y N N N N N N Y N Y N N Y N N N N N Y N N N N N N N N N N How many runs are there in these data?

In the sign test on a population median, what is done with values equal to the hypothesized median?

Concerning the Kruskal-Wallis test, the test statistic follows a chi-square distribution with degrees of freedom if H₀ is true and:

A two-sample t test with independent samples is the parametric version of a:

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).

As used in the runs test, a run is:

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?

Calculate the Spearman's rank correlation coefficient for the following rankings by x and y: ​ ​

Why Study Statistics

An Introduction to Statistics and Statistical Inference

Tables and Graphs for Summarizing Data

Numerical Summary Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Confidence Intervals Based on a Single Sample

Hypothesis Tests Based on a Single Sample

Confidence Intervals and Hypothesis Tests Based on Two Samples or Treatments

The Analysis of Variance

Correlation and Linear Regression

Categorical Data and Frequency Tables

Filters

When performing a Wilcoxon rank-sum test on the two independent samples shown here at α = 0.01, what is the alternative hypothesis? .

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).

Calculate the Spearman's rank correlation coefficient for the following rankings by x and y: