Deck 17: Introduction to Nonparametric Statistics

Question 1

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.

Answer 1

False

Question 2

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.

Answer 2

True

Question 3

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.

Answer 3

True

Question 4

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 5

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

Question 6

The Wilcoxon signed rank test can be a one or two-tailed test similar to hypothesis tests for population means.

Question 7

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 8

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 9

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 10

The t-test is not appropriate for ordinal data or if the populations examined are not believed to be approximately normally distributed and other methods such as the Wilcoxon test can be used.

Question 11

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

Question 12

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.

Question 13

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.

Question 14

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 15

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 16

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 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

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

Question 19

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

Question 20

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

Question 21

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

Question 22

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 23

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 24

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 25

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 26

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 27

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 28

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 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

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 31

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 32

A claim was recently made that stated that the median income for male and female graduates is the same for those graduating with an MBA degree. In order to test this claim using the Mann-Whitney U test, it is not necessary to select an equal number of males and females.

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

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

Question 35

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 36

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

Question 37

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 38

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 39

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 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

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 42

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 43

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 44

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 45

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 46

The critical value for a Kruskal Wallis test comes from the chi-square distribution.

Question 47

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 48

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 49

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 50

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 51

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 52

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

Question 53

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 54

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 55

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 56

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 57

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 58

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 59

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 60

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 61

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 = 2

Question 62

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 63

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 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 Seattle is:

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

Question 65

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 66

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 67

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

Question 68

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 69

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 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 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 71

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 72

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 73

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

A) Tests about a single population mean
B) Tests involving three or more population medians
C) Tests about a single population median
D) Tests about two or more population proportions

Question 74

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 75

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 76

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 77

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 78

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 79

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 80

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