Deck 17: Introduction to Nonparametric Statistics

Question 1

The procedure of the Wilcoxon signed rank test is the same for either small or large sample sizes.

Answer 1

False

Question 2

The Mann-Whitney U test can be used to test whether two independent populations have the same median so long as the data are measured on at least an ordinal scale.

Answer 2

True

Question 3

In conducting the Wilcoxon signed rank test,after collecting the sample data the next step is to find the sample median and subtract this value from each data value to obtain the deviations.

Answer 3

False

Question 4

The following null and alternative hypotheses are appropriate when using a Wilcoxon signed rank test.
H₀ : Population Median equals 14.5
H_{A :} Population Median is not equal to 14.5

Question 5

If a decision maker believes that the population is normally distributed and the data are known to be ratio level,then the either the t-test or the Wilcoxon signed rank test can be used to test null hypotheses about a single population mean.

Question 6

The basic logic of the Wilcoxon signed rank test is that if about half the data values fall above the hypothesized median,and about half fall below,the null hypothesis should not be rejected.

Question 7

Managers for a company that produces a weight loss product claim that the median weight lost over six weeks for people who use this product will be at least 20 pounds.The following data were collected from a sample of nine people who used the product.
Based on these data,the test statistic is W = 12.

Question 8

In the Wilcoxon signed rank test for testing about a single population median,if the sample size is large (n > 20),the test statistic can be approximated by the standard normal distribution.

Question 9

Recently,Major League Baseball officials stated that the median cost for a family of four to attend a baseball game including,parking,tickets,food,and drinks did not exceed $125.00.The following sample data were collected:
Assuming that the test of the owners' claim is going to be conducted using an alpha = .05 level,the critical value is t = 1.9432.

Question 10

All Wilcoxon signed rank tests are two-tailed tests since we are testing whether the population median is the exact center of the population distribution.

Question 11

Recently,Major League Baseball officials stated that the median cost for a family of four to attend a baseball game including,parking,tickets,food,and drinks did not exceed $125.00.The following sample data were collected:
Assuming that the test of the owners' claim is going to be conducted using an alpha = .05 level,the null hypothesis that the median cost does not exceed $125 should not be rejected.

Question 12

The Wilcoxon signed rank test should be used in place of the t-test whenever the sample size is less than 20.

Question 13

Recently,Major League Baseball officials stated that the median cost for a family of four to attend a baseball game including,parking,tickets,food,and drinks did not exceed $125.00.As long as the data are considered interval or ratio level,the t-test can be used to test MLB's claim.

Question 14

The Wilcoxon signed rank test is always a one-tail test with the rejection region in the upper tail.

Question 15

The Wilcoxon signed rank test is used for testing hypotheses about a population median if the data are at nominal level.

Question 16

The Wilcoxon signed rank test is used to test hypotheses about the population median.

Question 17

In a large sample test about a single population median,it is appropriate to employ the standard normal distribution so long as the population is also normally distributed.

Question 18

In the Wilcoxon signed rank test using either small or large sample sizes,any value that equals the hypothesized median is discarded from the analysis.

Question 19

Managers for a company that produces a weight loss product claim that the median weight lost over six weeks for people who use this product will be at least 20 pounds.The following data were collected from a sample of nine people who used the product.
In order to test the manager's claim,they will need to assume that the population is normally distributed.

Question 20

The Mann-Whitney U test is a nonparametric test that is used to test whether two related populations have the same median.

Question 21

The Wilcoxon Matched-Pairs Signed rank test is an alternative to the paired sample t-test when we are unwilling to assume that the populations are normally distributed.

Question 22

Recently,a study was done to determine whether the median speed on a section of highway is the same for cars versus trucks.A sample of 12 cars (n₁ = 12)and 15 trucks (n₂ = 15)was collected.If the Mann-Whitney U test is to be performed using an alpha = .05,the test critical U value is 49.

Question 23

A claim was recently made that stated that the median income for male and female graduates is the same for those graduating with a degree in operations management.In order to test this claim using the Mann-Whitney U test,the same number of males and females must be selected.

Question 24

In a Mann-Whitney U test,the test statistic will be equal to the sum of the ranks from sample one,or sample two,whichever is larger.

Question 25

A large sample Mann-Whitney U test should be used when the sample sizes exceed 20.

Question 26

A claim was recently made that stated that the median income for male and female graduates is the same for those graduating with a degree in operations management.The following sample data were collected:
In employing the Mann-Whitney U test,the U test statistic for the males is 43.5

Question 27

In conducting a Mann-Whitney U test when the sample size is greater than 20,the U test statistic can be assumed normally distributed.

Question 28

In employing the Mann-Whitney U test,the sample data from the two populations are first combined and the ranks of the data are determined,but we keep track of which population each ranked item came from.

Question 29

If a decision maker wishes to test to determine whether the medians are equal for two populations the Mann-Whitney U test is appropriate for either independent or dependent sampling situations.

Question 30

Recently,a study was done to determine whether the median speed on a section of highway is the same for cars versus trucks.A sample of 12 cars (n₁ = 12)and 15 trucks (n₂ = 15)was collected.If the Mann-Whitney U test is to be performed using an alpha = .05 and if the U test statistic is calculated to be 68,the null hypothesis should be rejected.

Question 31

A claim was recently made that stated that the median income for male and female graduates is the same for those graduating with a degree in operations management.The following sample data were collected:
In employing the Mann-Whitney U test,the sum of the ranks for the males is 53.5

Question 32

The Mann-Whitney U test is always a one-tailed test.

Question 33

The logic behind the Mann-Whitney U test is that if the hypothesis is true that the populations have equal central locations,then the sum of the ranks from each population will be approximately equal.

Question 34

A claim was recently made that stated that the median income for male and female graduates is the same for those graduating with a degree in operations management.The following sample data were collected:
In employing the Mann-Whitney U test,the U test statistic is 25.5

Question 35

In a Mann-Whitney U test,if the sample sizes are large then the test statistic can be approximated by the student's t-distribution.

Question 36

One of the assumptions associated with the Wilcoxon Matched-Pairs Signed Rank test is that the distribution of the population differences is symmetric about their median.

Question 37

One of the assumptions of the Mann-Whitney U test is that the population distributions are the same for shape and spread.

Question 38

In order to determine whether the median distance for the X-Special golf ball exceeds the median distance for the best-selling golf ball,six golfers were selected and asked to hit each ball with their driver.The distance was recorded.The following data were observed.
The appropriate null and alternative hypotheses are:
H₀ : ₁ ≤ ₂
H₀ : ₁ > ₂

Question 39

The critical value for a one-tailed Mann-Whitney U test with sample sizes of n₁ = 10 and n₂ = 10 is 23 for a 0.05 level of significance.

Question 40

In order to determine whether the median distance for the X-Special golf ball exceeds the median distance for the best-selling golf ball,six golfers were selected and asked to hit each ball with their driver.The distance was recorded.The following data were observed.
Based on these,the appropriate test is the Kruskal-Wallis one-way analysis of variance.

Question 41

A recent study was conducted to determine if any of three suppliers of electronic components has a different median delivery time on special orders.To test this,five orders were given to each supplier and the delivery days were recorded.These data are shown as follows:
If a Kruskal-Wallis test is to be performed,the critical value for a test conducted using an alpha = .05 level is χ² = 11.0705

Question 42

Kruskal-Wallis One-Way Analysis of Variance is the nonparametric counterpart to the one-way ANOVA procedure in which the assumptions of normally distributed populations with equal variances are satisfied.

Question 43

The critical value for a Kruskal Wallis test is an F value from the F-distribution.

Question 44

Assume that a Kruskal-Wallis test is being conducted to determine whether or not the medians of three populations are equal.The sum of rankings and the sample size for each group are below.
The value of the test statistic is H = 0.68

Question 45

A recent study was conducted to determine if any of three suppliers of electronic components has a different median delivery time on special orders.To test this,five orders were given to each supplier and the delivery days were recorded.These data are shown as follows:
If a Kruskal-Wallis test is to be performed,the number of degrees of freedom for determining the critical value is 2.

Question 46

The makers of furnace filters recently conducted a test to determine whether the median number of particulates that would pass through their four leading filters was the same.A random sample of 6 of each type of filter was used with the following data being recorded:
The Kruskal-Wallis test can be used in this case since it requires that the sample sizes be equal.

Question 47

The makers of furnace filters recently conducted a test to determine whether the median number of particulates that would pass through their four leading filters was the same.A random sample of 6 of each type of filter was used with the following data being recorded:
If the Kruskal-Wallis test is used,the test statistic is approximately H = 7.814

Question 48

In using the Kruskal-Wallis test the sample sizes for each population must be equal.

Question 49

In conducting the Wilcoxon Matched-Pairs Signed Rank test,the difference between each pair of values must be found prior to conducting any ranking.

Question 50

The makers of furnace filters recently conducted a test to determine whether the median number of particulates that would pass through their four leading filters was the same.A random sample of 6 of each type of filter was used with the following data being recorded:
If the managers are unwilling to assume that the populations are normally distributed,the appropriate test in this case would be the Mann-Whitney U test.

Question 51

Nonparametric statistical tests are used when:

A)the sample sizes are small.
B)we are unwilling to make the assumptions of parametric tests.
C)the standard normal distribution cannot be computed.
D)the population parameters are unknown.

Question 52

The makers of furnace filters recently conducted a test to determine whether the median number of particulates that would pass through their four leading filters was the same.A random sample of 6 of each type of filter was used with the following data being recorded:
If the Kruskal-Wallis test is used,the critical value for an alpha = .05 is 7.814

Question 53

When testing whether two paired populations have equal medians and the sample sizes are large,it is appropriate to convert the Wilcoxon Matched-Pairs Signed Rank test to a paired sample t-test.

Question 54

If you are interested in testing whether the median of a population is equal to a specific value,an appropriate test to use is:

A)the Mann-Whitney U test.
B)the t-test.
C)the Wilcoxon signed rank test.
D)the Wilcoxon Matched-Pairs Signed Rank test.

Question 55

The Kruskal-Wallis test is used to test whether the centers of 3 or more populations are equal so long as that is the only possible difference between the population distributions.

Question 56

A recent study was conducted to determine if any of three suppliers of electronic components has a different median delivery time on special orders.To test this,five orders were given to each supplier and the delivery days were recorded.These data are shown as follows:
If a Kruskal-Wallis test is to be performed,the sum of the rankings for Supplier 1 is 45.

Question 57

If a decision maker wishes to test whether four independent populations have the same center and is unwilling to make the assumption that the populations are normally distributed with equal variances,she can use the Kruskal-Wallis test.

Question 58

The distribution of T-values in the Wilcoxon Matched-Pairs Signed Rank test is approximately normal if the sample size (number of matched pairs)exceeds 25.

Question 59

In order to determine whether the median distance for the X-Special golf ball exceeds the median distance for the best-selling golf ball,six golfers were selected and asked to hit each ball with their driver.The distance was recorded.The following data were observed.
Based on these data,and testing at an alpha = 0.025 level,the critical value for the Wilcoxon Matched Pairs Signed Rank test is 2.

Question 60

The makers of furnace filters recently conducted a test to determine whether the median number of particulates that would pass through their four leading filters was the same.A random sample of 6 of each type of filter was used with the following data being recorded:
If the Kruskal-Wallis test is used with an alpha = .01,the null hypothesis should be rejected and the managers should conclude that the four filters do not allow an equal median number of particulates.

Question 61

Consider the situation in which a study was recently conducted to determine whether the median price of houses is the same in Seattle and Phoenix.The following data were collected. Given these data,if a Mann-Whitney U test is to be used,the U statistic for Seattle is:

A)45
B)35
C)22
D)14

Question 62

The General Electric service department believes that the median time for a service call should be 30 or fewer minutes.To test this,the following random sample of service times was collected: Given that the managers do not wish to make the assumption that the population is normally distributed,the critical value for the test about median service times,using a .05 level of significance,is:

A)5
B)40
C)8
D)37

Question 63

The General Electric service department believes that the median time for a service call should be 30 or fewer minutes.To test this,the following random sample of service times was collected: Given that the managers do not wish to make the assumption that the population is normally distributed,the test statistic for the Wilcoxon signed rank sum test is:

A)W = 43.0
B)W = 27.0
C)W = 18.0
D)None of the above

Question 64

Consider the situation in which a study was recently conducted to determine whether the median price of houses is the same in Seattle and Phoenix.The following data were collected. Given these data,if a Mann-Whitney U test is to be used,the U statistic for Phoenix is:

A)14
B)22
C)35
D)27

Question 65

Consider the situation in which a human resources manager wishes to determine whether the median number of days of sick leave per year is greater for female employees than for male employees.The following data represent random samples of males and females: If the manager is unwilling to assume that the populations are normally distributed,which of the following is the correct conclusion to reach if the test is conducted using a .05 level of significance?

A)Reject the null hypothesis
B)Conclude that females do have a higher median than males
C)Do not reject the null hypothesis
D)Conclude that males have a higher median than females

Question 66

Which of the following is not an assumption of the Mann-Whitney U test?

A)The sample sizes are equal.
B)The samples are independent.
C)The value measured is continuous.
D)The population distributions are the same for shape and spread.

Question 67

Which of the following tests would not be an example of nonparametric method?

A)Wilcoxon signed-rank test
B)Mann-Whitney U-Test
C)Kruskal-Wallis One-Way Analysis of Variance
D)χ² test

Question 68

The Wilcoxon signed rank test is used to test which of the following type of hypotheses?

A)Tests about a single population median
B)Tests involving three or more population medians
C)Tests about the variances of two or more populations
D)Tests about two or more population proportions

Question 69

In a large sample Mann-Whitney U test in which the sample size from the first population is 30 and the sample size from the second population is 40,which of the following is the expected U value if the null hypothesis of equal median values is true?

A)1,200
B)70
C)35
D)600

Question 70

The General Electric service department believes that the median time for a service call should be 30 or fewer minutes.To test this,the following random sample of service times was collected: Given that the managers do not wish to make the assumption that the population is normally distributed,the appropriate statistical test for testing about service times is:

A)the t-test.
B)the Kruskal-Wallis test.
C)the Wilcoxon signed rank sum test.
D)the F-test.

Question 71

In the finding the critical value for the Wilcoxon signed rank test,what does "n" represent?

A)The number of observations in the sample
B)The number of pairs
C)The number of nonzero deviations
D)The number of positive ranks

Question 72

A marketing firm is interested to know whether the median age of college students is 21 years.A sample of 80 college students is taken.Thirty of the students were under 21,45 of the students were over 21,and 10 were 21 years old.The conclusion is that

A)the median age of college students is significantly different from 21.
B)the median age of college students is not significantly different from 21.
C)the median age of college students is significantly older than from 21.
D)the median age of college students is significantly younger than from 21.

Question 73

Consider the situation in which a study was recently conducted to determine whether the median price of houses is the same in Seattle and Phoenix.The following data were collected. Given these data,if a Mann-Whitney U test is to be used,the test statistic is:

A)22
B)14
C)approximately 1.96
D)34

Question 74

Which of the following is not a step involved in the Wilcoxon signed rank test?

A)Find the deviations from the hypothesized median
B)Rank the deviations
C)Convert the deviations to absolute values
D)Find the deviations from the sample median

Question 75

Consider the situation in which a human resources manager wishes to determine whether the median number of days of sick leave per year is the same for female employees as for male employees.The following data represent random samples of males and females: If the manager is unwilling to assume that the populations are normally distributed,which of the following would be the appropriate null hypothesis to be tested?

A)H₀ : μ = 0
B)H₀ :
= 0
C)H₀ : μ₁ = μ₂
D)H₀ :
₁ =

Question 76

Under what circumstances should the standard normal distribution be used when employing the Mann-Whitney U test?

A)When the sample sizes are equal from the two populations
B)When the sample sizes are greater than 20
C)When the populations are normally distributed
D)You would never use the standard normal distribution.

Question 77

Recently,a legislative committee commissioned a study of incomes in a western state.At issue was whether the ratings of the legislature's performance differed between rural citizens and city residents.A random sample of 25 city residents and 35 rural residents was asked to rate the performance of the legislature on a scale of 1 to 100.The analysts believe that the population distribution of ratings would be highly skewed so they decided to use the Mann-Whiney U test to test whether there is a difference in median ratings by the two groups.Given this information,which of the following is the correct critical value if the test is to be conducted at the .10 level of significance?

A)z = 1.96
B)t = 2.0357
C)U = 437.5
D)z = 1.645

Question 78

When the Mann-Whitney U test is performed,which of the following is true?

A)We assume that the populations are normally distributed.
B)We are interested in testing whether the medians from two populations are equal.
C)The data are nominal level.
D)The samples are independent.

Question 79

Consider the situation in which a study was recently conducted to determine whether the median price of houses is the same in Seattle and Phoenix.The following data were collected. Given these data,if a Mann-Whitney U test is to be used,the sum of the ranks for Seattle is:

A)43
B)35
C)25.5
D)40

Question 80

Assume you are conducting a two-tailed Mann-Whitney U test for a small sample and have found that U₁ = 58 and U₂ = 86.What is the value of the test statistic?

A)58
B)86
C)72
D)144