Deck 18: Nonparametric Methods

Question 1

A nonparametric test for the equivalence of two populations would be used instead of a parametric test for the equivalence of the population parameters if

A)the samples are very large
B)the samples are not independent
C)no information about the populations is available
D)The parametric test is always used in this situation.

Answer 1

C

Question 2

The level of measurement that is a label for the purpose of identifying an item is

A)ordinal measurement
B)ratio measurement
C)nominal measurement
D)internal measurement

Answer 2

C

Question 3

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

A)Mann-Whitney-Wilcoxon test
B)Wilcoxon signed-rank test
C)sign test
D)t test

Answer 3

D

Question 4

Exhibit 18-1
Ten people were given two types of cereal, Brand X and Brand Y. Three people preferred Brand X, 5 people preferred Brand Y, and 2 people were undecided. We want to determine whether or not the two products are equal.
Refer to Exhibit 18-1. The null hypothesis should be

A)rejected
B)not rejected
C)revised
D)None of these alternatives is correct.

Question 5

Statistical methods that generally require very few, if any, assumptions about the population distribution are known as

A)parametric
B)nonparametric
C)free methods
D)None of these alternatives is correct.

Question 6

A nonparametric test would be used if

A)nominal data is available
B)interval data is available
C)it is known that the population is normally distributed
D)None of these alternatives is correct.

Question 7

Exhibit 18-1
Ten people were given two types of cereal, Brand X and Brand Y. Three people preferred Brand X, 5 people preferred Brand Y, and 2 people were undecided. We want to determine whether or not the two products are equal.
Refer to Exhibit 18-1. The hypothesis is to be tested at the 5% level. The decision rule is not to reject the null hypothesis if

A)-1.96 < A < 1.96
B)-2.262 < t < 2.262
C)the number of "+" signs is greater than or equal to 2 and less than or equal to 6
D)the number of "+" signs is greater than or equal to 1 and less than or equal to 7

Question 8

Exhibit 18-1
Ten people were given two types of cereal, Brand X and Brand Y. Three people preferred Brand X, 5 people preferred Brand Y, and 2 people were undecided. We want to determine whether or not the two products are equal.

-Refer to Exhibit 18-1. The null hypothesis that is being tested is

A)H₀: $\mu$ = 5
B)H₀: $\mu$ = 0.5
C)H₀: p = 5
D)H₀: p = 0.5

Question 9

A nonparametric method for determining the differences between two populations based on two matched samples where only preference data is required is the

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

Question 10

Exhibit 18-2
Students in statistics classes were asked whether they preferred a 10-minute break or to get out of class 10 minutes early. In a sample of 150 students, 40 preferred a 10-minute break, 80 preferred to get out 10 minutes early, and 30 had no preference. We want to determine if there is a difference in students' preferences.
Refer to Exhibit 18-2. The hypothesis is to be tested at the 5% level of significance. The decision rule is not to reject the null hypothesis if

A)-1.96 < z < 1.96
B)-1.645 < z < 1.645
C)z > 1.96 or z < -1.96
D)the number of "+" signs is greater than or equal to 20 and less than or equal to 130

Question 11

The level of measurement that allows for the rank ordering of data items is

A)nominal measurement
B)ratio measurement
C)interval measurement
D)ordinal measurement

Question 12

A nonparametric version of the Parametric analysis of variance test is the

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

Question 13

Exhibit 18-1
Ten people were given two types of cereal, Brand X and Brand Y. Three people preferred Brand X, 5 people preferred Brand Y, and 2 people were undecided. We want to determine whether or not the two products are equal.
Refer to Exhibit 18-1. To test the null hypothesis, the appropriate probability distribution to use is

A)normal
B)chi-square
C)Poisson
D)binomial

Question 14

Statistical methods that require assumptions about the population are known as

A)distribution free
B)nonparametric
C)either distribution free of nonparametric
D)parametric

Question 15

When ranking combined data in a Wilcoxon signed rank test, the data that receives a rank of 1 is the

A)lowest value
B)highest value
C)middle value
D)average of the highest and the lowest of values

Question 16

Exhibit 18-2
Students in statistics classes were asked whether they preferred a 10-minute break or to get out of class 10 minutes early. In a sample of 150 students, 40 preferred a 10-minute break, 80 preferred to get out 10 minutes early, and 30 had no preference. We want to determine if there is a difference in students' preferences.
Refer to Exhibit 18-2. The test statistic based on the number of students who preferred to get out early equals

A)-3.65
B)0.67
C)0.82
D)3.65

Question 17

Exhibit 18-2
Students in statistics classes were asked whether they preferred a 10-minute break or to get out of class 10 minutes early. In a sample of 150 students, 40 preferred a 10-minute break, 80 preferred to get out 10 minutes early, and 30 had no preference. We want to determine if there is a difference in students' preferences.
Refer to Exhibit 18-2. To test the null hypothesis, the appropriate probability distribution to use is the

A)normal
B)chi-square
C)t distribution
D)binomial

Question 18

Exhibit 18-2
Students in statistics classes were asked whether they preferred a 10-minute break or to get out of class 10 minutes early. In a sample of 150 students, 40 preferred a 10-minute break, 80 preferred to get out 10 minutes early, and 30 had no preference. We want to determine if there is a difference in students' preferences.
Refer to Exhibit 18-2. The null hypothesis should be

A)rejected
B)not rejected
C)revised
D)None of these alternatives is correct.

Question 19

The labeling of parts as "defective" or "non-defective" is an example of

A)ordinal data
B)ratio data
C)interval data
D)nominal data

Question 20

The Spearman rank-correlation coefficient is

A)a correlation measure based on the average of data items
B)a correlation measure based on rank-ordered data for two variables
C)a correlation measure based on the median of data items
D)None of these alternatives is correct.

Question 21

Exhibit 18-5
Forty-one individuals from a sample of 60 indicated they oppose legalized abortion. We are interested in determining whether or not there is a significant difference between the proportions of opponents and proponents of legalized abortion.
Refer to Exhibit 18-5. The hypothesis is to be tested at the 5% level. The decision rule is not to reject the null hypothesis if

A)-1.96 < z < 1.96
B)-3 < t < 3
C)F > 5
D)Chi-square > 5

Question 22

Exhibit 18-4
It has been hypothesized that there is no difference in the mathematical accuracy of men and women. A sample of men and women were given math tests. The scores on the tests are given below.
Refer to Exhibit 18-4. To test the null hypothesis, the appropriate probability distribution to use is

A)normal
B)chi-square
C)t distribution
D)binomial

Question 23

Exhibit 18-5
Forty-one individuals from a sample of 60 indicated they oppose legalized abortion. We are interested in determining whether or not there is a significant difference between the proportions of opponents and proponents of legalized abortion.
Refer to Exhibit 18-5. The null hypothesis should be

A)rejected
B)not rejected
C)Not enough information is given to answer this question.
D)None of these alternatives.

Question 24

Exhibit 18-3
A company advertises that food preparation time can be significantly reduced with the Handy Dandy Slicer. A sample of 12 individuals prepared the ingredients for a meal with and without the slicer. You are given the preparation times below.
Refer to Exhibit 18-3. The null hypothesis should be

A)rejected
B)not rejected
C)revised
D)None of these alternatives is correct.

Question 25

Exhibit 18-2
Students in statistics classes were asked whether they preferred a 10-minute break or to get out of class 10 minutes early. In a sample of 150 students, 40 preferred a 10-minute break, 80 preferred to get out 10 minutes early, and 30 had no preference. We want to determine if there is a difference in students' preferences.
If a null hypothesis that states that two populations are identical is rejected using a nonparametric test, then it is safe to assume that

A)neither the means nor the variances are equal
B)the means of the populations are not the same
C)the variances of the populations are not the same
D)We cannot be sure of the way in which the populations differ from each other.

Question 26

Exhibit 18-3
A company advertises that food preparation time can be significantly reduced with the Handy Dandy Slicer. A sample of 12 individuals prepared the ingredients for a meal with and without the slicer. You are given the preparation times below.
Refer to Exhibit 18-3. The hypothesis is to be tested at the 5% level of significance. The decision rule is not to reject the null hypothesis if

A)-1.96 < z < 1.96
B)-1.645 < z < 1.645
C)z > 1.96 or z < -1.96
D)the number of "+" signs is greater than or equal to 2 but less than or equal to 8

Question 27

Exhibit 18-3
A company advertises that food preparation time can be significantly reduced with the Handy Dandy Slicer. A sample of 12 individuals prepared the ingredients for a meal with and without the slicer. You are given the preparation times below.
Refer to Exhibit 18-3. The test statistic equals

A)-0.812 or 0.812
B)-0.889 or 0.889
C)-10 or 10
D)-20 or 20

Question 28

Exhibit 18-4
It has been hypothesized that there is no difference in the mathematical accuracy of men and women. A sample of men and women were given math tests. The scores on the tests are given below.
Refer to Exhibit 18-4. The null hypothesis is to be tested at the 5% level. The decision rule is not to reject the null hypothesis if

A)-1.96 < z < 1.96
B)-1.645 < z < 1.645
C)z > 1.96 or z < -1.96
D)the number of "+" signs is greater than or equal to 2 but less than or equal to eight

Question 29

Exhibit 18-4
It has been hypothesized that there is no difference in the mathematical accuracy of men and women. A sample of men and women were given math tests. The scores on the tests are given below.

-Refer to Exhibit 18-4. Calculate a Spearman rank-correlation coefficient for 20 pairs of data when $\Sigma$ d_i² = 50.

A)0.0063
B)0.0376
C)0.9624
D)0.9937

Question 30

Exhibit 18-5
Forty-one individuals from a sample of 60 indicated they oppose legalized abortion. We are interested in determining whether or not there is a significant difference between the proportions of opponents and proponents of legalized abortion.

-Refer to Exhibit 18-5. The null hypothesis that is being tested is

A)H₀: $\mu$ = 5
B)H₀: $\mu$ = 0.5
C)H₀: p = 5
D)H₀: p = 0.5

Question 31

Exhibit 18-3
A company advertises that food preparation time can be significantly reduced with the Handy Dandy Slicer. A sample of 12 individuals prepared the ingredients for a meal with and without the slicer. You are given the preparation times below.
Refer to Exhibit 18-3. To test the null hypothesis, the appropriate probability distribution to use is

A)normal
B)chi-square
C)t distribution
D)binomial

Question 32

The Spearman rank-correlation coefficient for 20 pairs of data when $\Sigma$ d_i² = 50 is.

A)0.0063
B)0.0376
C)0.9624
D)0.9937

Question 33

Exhibit 18-5
Forty-one individuals from a sample of 60 indicated they oppose legalized abortion. We are interested in determining whether or not there is a significant difference between the proportions of opponents and proponents of legalized abortion.

-Refer to Exhibit 18-5. $\sigma$ in this problem is

A)15
B)5.47
C)3.87
D)7.45

Question 34

Excel's ____ function can be used to conduct a sign test.

A)POISSON.DIST
B)T.INV
C)BINOM.DIST
D)CHISQ.DIST.RT

Question 35

Exhibit 18-5
Forty-one individuals from a sample of 60 indicated they oppose legalized abortion. We are interested in determining whether or not there is a significant difference between the proportions of opponents and proponents of legalized abortion.

-Refer to Exhibit 18-5. $\mu$ in this situation is

A)60
B)30
C)41
D)2

Question 36

Excel's ____ function can be used to conduct the Kruskal-Wallis test.

A)POISSON.DIST
B)BINOM.DIST
C)CHISQ.DIST.RT
D)NORM.S.DIST

Question 37

Exhibit 18-5
Forty-one individuals from a sample of 60 indicated they oppose legalized abortion. We are interested in determining whether or not there is a significant difference between the proportions of opponents and proponents of legalized abortion.
Refer to Exhibit 18-5. The conclusion is that there

A)is no significant difference between the proportions
B)is a significant difference between the proportions
C)could be a difference in proportions, depending on the sample size
D)None of these alternatives is correct.

Question 38

Excel's ____ function can be used to conduct the Wilcoxon signed-rank test.

A)POISSON.DIST
B)BINOM.DIST
C)CHISQ.DIST.RT
D)NORM.S.DIST

Question 39

Exhibit 18-4
It has been hypothesized that there is no difference in the mathematical accuracy of men and women. A sample of men and women were given math tests. The scores on the tests are given below.
Refer to Exhibit 18-4. The test statistic equals (using the women as population 1)

A)-5.246
B)0.176
C)0.722
D)2.5

Question 40

Exhibit 18-5
Forty-one individuals from a sample of 60 indicated they oppose legalized abortion. We are interested in determining whether or not there is a significant difference between the proportions of opponents and proponents of legalized abortion.
Refer to Exhibit 18-5. The test statistics is

A)3.87
B)2.84
C)60
D)0.5

Question 41

The following data show the test scores of six individuals on a standardized test before and after attending a preparation seminar for the test.
Use Wilcoxon Signed-Rank test in order to determine whether or not the seminar has been effective. Hint: This is a one tailed test. Let $\alpha$ = 0.05.

Question 42

For the Wilcoxon signed-rank test, differences of 0 are

A)discarded
B)assigned a rank of n/2
C)assigned a rank of n
D)assigned a rank of n + 1

Question 43

The following data show the preference of 20 people for a candidate to a public office. A "+" indicates a preference for the Democratic candidate, and a "-" indicates a preference for the Republican candidate.
With $\alpha$ = 0.05, test for a significant difference in the preference for the candidates.

Question 44

Exhibit 18-6
It is believed that the median yearly income in a suburb of Atlanta is $70,000. A sample of 67 residents was taken. Thirty-eight had yearly incomes above $70,000, 26 had yearly incomes below $70,000, and 3 had yearly incomes equal to $70,000. The null hypothesis to be tested is H₀: median = $70,000.
Refer to Exhibit 18-6. To test the null hypothesis, the appropriate probability distribution to use is

A)normal
B)chi-square
C)t distribution
D)binomial

Question 45

Ten drivers were asked to drive two models of a car. Each car was given one gallon of gasoline. The distance that each automobile traveled on a gallon of gasoline is shown below.
At $\alpha$ = 0.05, what can be concluded about the performance of the two models?

Question 46

Refer to Exhibit 18-6. The p-value for this test is

A)0.4332
B)0.8664
C)0.0668
D)0.1336

Question 47

In a sample of 300 shoppers, 160 indicated they prefer fluoride toothpaste, 120 favored nonfluoride, and 20 were indifferent. At a 0.05 level of significance, test for a difference in the preference for the two kinds of toothpaste.

Question 48

Refer to Exhibit 18-6. The null hypothesis should be

A)rejected
B)not rejected
C)revised
D)None of these alternatives is correct.

Question 49

Refer to Exhibit 18-6. The test statistic has a value of

A)1.00
B)1.50
C)2.00
D)2.50

Question 50

In a sample of 120 people, 50 indicated that they prefer domestic automobiles, 60 said they prefer foreign-made cars, and 10 indicated no difference in their preference. At a 0.05 level of significance, determine if there is evidence of a significant difference in the preferences for the two makes of automobiles.

Question 51

If the assumption can be made that the populations all have the same shape, the Kruskal-Wallis test becomes

A)a test of the skewness of the k populations
B)a test of the variances of the k populations
C)a test of the medians of the k populations
D)a test of the means of the k populations

Question 52

Two employers (A and B) ranked five candidates for a new position. Their rankings of the candidates are shown below.
Compute the Spearman rank-correlation and test it for significance. Let $\alpha$ = 0.05.

Question 53

Ten administrative assistants were sent to take a typing efficiency course. The following data show the typing speeds of the administrative assistants before and after the course.
At $\alpha$ = 0.05, what can be concluded about the effectiveness of the course?

Question 54

From the courthouse records, it is found that in 60 divorce cases, the filing for divorce was initiated by the wife 41 times. Using the sign test, test for a difference in filing between husband and wives. Let $\alpha$ = 0.05

Question 55

For the Wilcoxon signed-rank test, ties among absolute differences are assigned the

A)lowest of their ranks
B)average of their ranks
C)highest of their ranks
D)sum of their ranks

Question 56

Fifteen people were asked to indicate their preference for domestic versus imported cars. The following data showed their preferences.
With $\alpha$ = 0.06, test for a significant difference in the preferences for cars. A "+" indicates a preference for imported cars.

Question 57

Nonparametric methods which can be used to make inferences about a population without requiring an assumption about the distribution of the population are called

A)continuity-correction methods
B)non-probabilistic methods
C)distribution-free methods
D)non-quantitative methods

Question 58

Independent random samples of ten day students and ten evening students at a university showed the following age distributions.
Use $\alpha$ = 0.05 and test for any significant differences in the age distribution of the two populations.

Question 59

Refer to Exhibit 18-6. The mean and the standard deviation (respectively) for this test about the median are

A)32 and 4
B)32 and 16
C)33.5 and 4
D)33.5 and 16

Question 60

The sales records of two branches of a department store over the last 12 months are shown below. (Sales figures are in thousands of dollars.)
Use $\alpha$ = 0.05 and test to determine if there is a significant difference in the populations of the sales of the two branches.

Question 61

Two groups of students were asked to rank the activities sponsored by the Student Government Association on campus. The following show their rankings.
Determine the Spearman rank-correlation coefficient and test for a significant correlation with $\alpha$ = 0.05.

Question 62

A clothing manufacturer purchased some newly designed sewing machines in the hopes that production would be increased. The production records of a random sample of workers are shown below. Use the Wilcoxon signed-rank test to determine whether the new machines have significantly increased production. Use the .05 level of significance.

Question 63

The manager of a company believes that differences in sales performance depend upon the salesperson's age. Independent samples of salespeople were taken and their weekly sales record is reported below.
a.State the null and alternative hypotheses.
b.Test the null hypothesis at the 5% level.

Question 64

We want to see if the workers on the day and night shifts differ significantly in their productivity levels. A sample of workers from both shifts was taken.
a.State the null and alternative hypotheses.
b.Test the null hypothesis at the 5% level of significance.

Question 65

A comprehensive statistics examination is given to 16 students in order to determine whether or not there is a significant difference in the performance of students majoring in the various disciplines of Business Administration. The following data show the scores of the 16 students (5 majoring in accounting, 6 majoring in management, and 5 majoring in marketing).
At $\alpha$ = 0.05 level of significance, test to see if there is a significant difference in the performance of the students in the three majors.

Question 66

A survey of male and female students showed the following ranking of 12 professors in the management department:
Do the rankings given by the female students agree with the rankings given by the male students? Use $\alpha$ = 0.05.

Question 67

A market researcher is asked to compare the responses to two questions on a customer satisfaction survey that was completed by 20 consumers. The first question asks the respondents to rate the product's quality and the second question asks the respondents to rate the product's ease of use. The results follow. Use Excel to calculate the Spearman correlation coefficient and then interpret its value.

Question 68

Two faculty members ranked 12 candidates for scholarships. Calculate the Spearman rank-correlation coefficient and test whether the professors had significantly different rankings. Use the .02 level of significance.

Question 69

Three managers received the following performance ratings from a group of 15 employees.
Use Excel to perform the appropriate test at $\alpha$ = .05 to determine whether there is a significant difference in the performance ratings for the mangers.

Question 70

The president of a company wants to see if the new anti-smoking campaign is having any influence on his employees. A sample of 100 employees who smoked prior to the campaign is taken. Thirty-six employees said they smoked less, 15 employees said they smoked more, and 49 employees said there was no change.
a.State the null and alternative hypotheses.
b.Test the null hypothesis at the 1% level of significance.

Question 71

A real estate agency conducts a study to determine if the median selling price of homes in a particular neighborhood has changed since last year. Last year the median selling price was $188,500. The agency randomly selects 20 recently sold homes in that particular neighborhood and finds that 14 of the homes sold for more than $188,500 and that 6 of the homes sold for less than $188,500. Use Excel to conduct the appropriate hypothesis test at $\alpha$ = .10.

Question 72

Two movie critics have independently ranked the top 20 movies of the year. Their rankings follow. Use Excel to calculate the Spearman correlation coefficient and then interpret its value.

Question 73

Three universities in your state have decided to administer the same comprehensive examination to the recipients of MBA degrees. From each institution, a random sample of MBA recipients has been selected and given the test. The following table shows the scores of the students from each university.
Use the Kruskal-Wallis test to determine if there is a significant difference in the average scores of the students from the three universities. Let $\alpha$ = 0.01.

Question 74

A market research firm is conducting a study to determine which of two package designs for a liquid soap product potential customers prefer, the current design (A) or a new design (B). A sample of 40 potential customers is taken. The results follow.
Use Excel to conduct the appropriate hypothesis test at $\alpha$ = .05 to determine if the data indicate that there is a difference in preference between the two designs.

Question 75

Two faculty members (X and Y) ranked five candidates for scholarships. The rankings are shown below.
Compute the Spearman rank-correlation and test it for significance. Let $\alpha$ = 0.05.

Question 76

A market research firm is conducting a study to determine which of two package designs for a liquid soap product potential customers prefer, the current design (A) or a new design (B). A sample of 20 potential customers is taken. The results follow.
Use Excel to conduct the appropriate hypothesis test at $\alpha$ = .05 to determine if the data indicate that there is a difference in preference between the two designs.

Question 77

A PTA group wishes to determine whether a barrage of letters sent to the local station has reduced the amount of violence broadcast between the hours of 4 and 9 P.M. The results of a survey of viewers are given here.
Carry out a sign test to determine whether or not the letters were effective in reducing the amount of violence during the 4 to 9 p.m. period. Use a .05 level of significance. Be sure to state the null and alternative hypotheses.

Question 78

A large company that develops, distributes, and grades national standardized examinations wants to pilot test a new examination. A group of 20 students is used for the study. Each student is given two versions of the examination. The order in which the students take the examinations is randomly assigned. The students' scores follow.
Use Excel to test to determine if the differences in the students' scores between the two versions of the examination are significantly different. Use $\alpha$ = .10.

Question 79

Two individuals were asked to rank the performances of eight different automobiles. The following show their rankings.
Determine the Spearman rank-correlation coefficient and test for a significant correlation with $\alpha$ = 0.05.

Question 80

It is believed that 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.
a.State the null and alternative hypotheses.
b.Test the null hypothesis at the 1% level of significance.