Deck 19: Nonparametric Methods

Question 1

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

Answer 1

D

Question 2

A collection of statistical methods that generally requires very few,if any,assumptions about the population distribution is known as

A)parametric methods
B)nonparametric methods
C)distribution-fixed methods
D)normal

Answer 2

B

Question 3

The speed of an automobile is an example of a variable that uses the

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

Answer 3

A

Question 4

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

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

Question 5

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

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

Question 6

Parametric methods are statistical methods that

A)require some assumptions about the population
B)require no assumptions about the population
C)only deal with small samples
D)considers the sign of two matched samples

Question 7

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 8

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 9

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 10

The scale of measurement that is used to rank order the observation for a variable is called the

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

Question 11

A sign test is a

A)parametric method for determining the differences between two populations based on two matched samples
B)nonparametric method for determining the differences between two populations based on two matched samples
C)nonparametric method for determining the differences between two or more populations based on two or more matched samples
D)parametric method for determining the differences between two or more populations based on two or more matched samples

Question 12

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 13

In a questionnaire,respondents are asked to mark their marital status.Marital status is an example of the

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

Question 14

On a teacher evaluation form students are asked to rate their professor's performance as excellent,very good,good,and poor.This is an example of the

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

Question 15

Temperature is an example of a variable that uses

A)the ratio scale
B)the interval scale
C)the ordinal scale
D)either the ratio or the ordinal scale

Question 16

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

Question 17

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 18

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 19

The collection of statistical methods that require assumptions about the population is known as

A)distribution free methods
B)nonparametric methods
C)small populations
D)parametric methods

Question 20

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 21

Exhibit 19-2
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 19-2.The mean and the standard deviation of the sampling distribution of the number of students who preferred to get out early are

A)50 and 30
B)60 and 30
C)50 and 5.478
D)60 and 5.478

Question 22

Exhibit 19-2
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 19-2.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 23

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.

Question 24

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 25

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 19-3
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 19-3.The test statistic has a value of

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

Question 27

Exhibit 19-4
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 19-4.To test the null hypothesis,the appropriate probability distribution to use is

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

Question 28

Exhibit 19-3
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 19-3.The null hypothesis should be

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

Question 29

Exhibit 19-3
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 19-3.To test the null hypothesis,the appropriate probability distribution to use is

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

Question 30

Exhibit 19-2
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 19-2.The test statistic based on the number of students who preferred to get out early equals

A)1.825
B)0.67
C)0.82
D)3.65

Question 31

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 32

Exhibit 19-1
Fifteen people were given two types of cereal,Brand X and Brand Y.Two people preferred Brand X and thirteen people preferred Brand Y.We want to determine whether or not customers prefer one brand over the other.

-Refer to Exhibit 19-1.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 33

Exhibit 19-2
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 19-2.The p-value for testing the hypotheses is

A)less than 0.002
B)between 0.002 and 0.05
C)between 0.05 and 0.10
D)greater than 0.10

Question 34

Exhibit 19-1
Fifteen people were given two types of cereal,Brand X and Brand Y.Two people preferred Brand X and thirteen people preferred Brand Y.We want to determine whether or not customers prefer one brand over the other.
Refer to Exhibit 19-1.The p-value for this test is

A)0.0005
B)0.001
C)0.0037
D)0.0074

Question 35

Exhibit 19-3
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 19-3.The p-value for this test is

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

Question 36

Exhibit 19-3
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 19-3.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 37

Exhibit 19-2
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 19-2.To test the null hypothesis,the appropriate probability distribution to use is the

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

Question 38

Exhibit 19-2
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 19-2.The null hypothesis should be

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

Question 39

Exhibit 19-1
Fifteen people were given two types of cereal,Brand X and Brand Y.Two people preferred Brand X and thirteen people preferred Brand Y.We want to determine whether or not customers prefer one brand over the other.
Refer to Exhibit 19-1.At 95% confidence,the null hypothesis should

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

Question 40

Exhibit 19-1
Fifteen people were given two types of cereal,Brand X and Brand Y.Two people preferred Brand X and thirteen people preferred Brand Y.We want to determine whether or not customers prefer one brand over the other.
Refer to Exhibit 19-1.To test the null hypothesis,the appropriate probability distribution to use is

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

Question 41

Exhibit 19-6
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 19-6.p-value is

A)0.0023
B)0.0046
C)0.4954
D)0.4977

Question 42

Exhibit 19-5
It has been hypothesized that there is no difference in the mathematical ability of men and women.To test this hypothesis,it was decided to use the Mann-Whitney-Wilcoxon test.A sample of men and women were given math tests.The scores on the tests are given below.


-Refer to Exhibit 19-5.The standard deviation ( $\sigma$ _T)is

A)10
B)11.5
C)14.2
D)110

Question 43

The monthly sales records of two branches of a department store (Branch A and Branch B)over the last year (12 months)were gathered.It was decided to use the Mann-Whitney-Wilcoxon test to determine if there has been a significant difference between the sales of the two branches.
a.Provide the hypotheses for this test.
b.Compute the mean $\mu$ _T.
c.Compute the standard deviation $\sigma$ _T.
d.The sum of the ranks for branch A was determined to be 184.5.Compute the test statistic Z.
e.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 44

Exhibit 19-6
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 19-6. $\sigma$ in this problem is

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

Question 45

Exhibit 19-4
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 19-4.The p-value for this test is

A)0.3133
B)0.6266
C)0.3734
D)0.8167

Question 46

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 47

Exhibit 19-4
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 19-4.The test statistic equals

A)-0.81 or 0.81
B)-0.89 or 0.89
C)-10 or 10
D)-20 or 20

Question 48

Exhibit 19-6
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 19-6.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 49

Exhibit 19-5
It has been hypothesized that there is no difference in the mathematical ability of men and women.To test this hypothesis,it was decided to use the Mann-Whitney-Wilcoxon test.A sample of men and women were given math tests.The scores on the tests are given below.


-Refer to Exhibit 19-5.The mean ( $\mu$ _T)is

A)10
B)110
C)66
D)55

Question 50

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. )We want to use the Mann-Whitney-Wilcoxon test to determine if there is a significant difference in the sales of the two branches.

a.Compute the sum of the ranks (T)for branch A.
b.Compute the mean $\mu$ _T.
c.Compute $\sigma$ _T.
d..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 51

Independent random samples of the scores of 10 daily quizzes from day students and 15 quizzes from evening students were gathered.It was decided to use the Mann-Whitney-Wilcoxon test to determine if there is a significant difference between the scores of the two groups of students.
a.Provide the hypotheses for this test.
b.Compute the mean $\mu$ _T.
c.Compute the standard deviation $\sigma$ _T.
d.The sum of the ranks for the day students was determined to be 184.5.Compute the test statistic Z.
e.Use $\alpha$ = 0.05 and test to determine if there is a significant difference in the populations of the scores of the two groups.

Question 52

Exhibit 19-4
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 19-4.The null hypothesis should

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

Question 53

Exhibit 19-6
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 19-6.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 54

Exhibit 19-6
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 19-6. $\mu$ in this situation is

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

Question 55

Exhibit 19-5
It has been hypothesized that there is no difference in the mathematical ability of men and women.To test this hypothesis,it was decided to use the Mann-Whitney-Wilcoxon test.A sample of men and women were given math tests.The scores on the tests are given below.

Refer to Exhibit 19-5.To test the null hypothesis,the appropriate probability distribution to use is

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

Question 56

Independent random samples of ten day students and ten evening students at a university showed the following age distributions.We want to use the Mann-Whitney-Wilcoxon test to determine if there is a significant difference in the age distribution of the two groups.

a.Compute the sum of the ranks (T)for the day students.
b.Compute the mean $\mu$ _T.
c.Compute $\sigma$ _T.
d..Use $\alpha$ = 0.05 and test for any significant differences in the age distribution of the two populations.

Question 57

In a sample of 400 people,250 indicated that they prefer domestic wines,while 140 said they prefer European wines,and 10 indicated no preference.We want to use the sign test to determine if there is evidence of a significant difference in the preferences for the two types of wine.
a.Provide the hypotheses to be tested.
b.Compute the mean.
c.Compute the standard deviation.
d..At 95% confidence,test to determine if there is evidence of a significant difference in the preferences for the two types of wine.

Question 58

Exhibit 19-6
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 19-6.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 59

Exhibit 19-6
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 19-6.The test statistics is

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

Question 60

In a sample of 200 racquetball players,120 indicated they prefer Penn racquetballs,75 favored Ektelon,and 5 were indifferent.We want to use the sign test to determine if there is evidence of a significant difference in the preferences for the two types of racquetballs.
a.Provide the hypotheses to be tested.
b.Compute the mean.
c.Compute the standard deviation.
d..At 95% confidence,test to determine if there is evidence of a significant difference in the preferences for the two types of racquetballs.

Question 61

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 62

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 63

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 64

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 a .05 level of significance.

Question 65

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 P.M.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 66

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 67

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 68

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 69

Fifteen people were asked to indicate their preference for domestic versus imported cars.The following data showed their preferences.

With $\alpha$ = 0.05,test for a significant difference in the preferences for cars.A "+" indicates a preference for imported cars.

Question 70

The manager of a company believes that differences in sales performance depends 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.At 95% confidence,test the hypotheses.

Question 71

Test scores of ten individuals before and after a training program are shown below.

At $\alpha$ = 0.05,what can be concluded about the effectiveness of the training program?

Question 72

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 73

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 74

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 75

Two individuals were asked to rank the performances of eight different automobiles.The following show their rankings.

Determine the Spearman rank-correlation coefficient;and at 95% confidence,test for its significance.

Question 76

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 77

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.

Question 78

Two faculty members ranked 12 candidates for scholarships.Calculate the Spearman rank-correlation coefficient and test it for significance.Use a .02 level of significance.

Question 79

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 the Wilcoxon Signed-Rank test in order to determine whether or nor the seminar has been effective.Hint: This is a one tailed test.Let $\alpha$ = 0.05.

Question 80

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.