Deck 17: Nonparametric Methods

Question 1

Parametric tests,such as F and t tests,are more powerful than their nonparametric counterparts if the assumptions needed to perform the parametric test are not violated.

Answer 1

True

Question 2

A parametric test is always more powerful than its nonparametric counterpart.

Answer 2

False

Question 3

Which one of the following nonparametric methods can be used to compare more than two independent populations in a single test?

A) Wilcoxon signed ranks test
B) sign test
C) Kruskal-Wallis test
D) Wilcoxon rank sum test
E) Spearman's test

Answer 3

Kruskal-Wallis test

Question 4

The sign test is a test about a population median that is valid for any sample size and population shape.

Question 5

Which of the following statements about nonparametric methods is correct?

A) Nonparametric tests are only used in cases where parametric tests such as t or F do not exist.
B) Nonparametric tests should always be used when one is available,because they are easier to apply then their parametric counterparts.
C) Nonparametric tests are useful alternatives to parametric tests such as t or F when certain assumptions required by parametric tests are violated.
D) Nonparametric tests are only used if the data come from independent samples.

Question 6

If you have data that consist of matched pairs collected from two dependent populations,then it may be appropriate to use the Wilcoxon signed ranks test.

Question 7

Nonparametric tests can be more powerful than the corresponding t or F tests if the population distribution is highly skewed or nonnormal.

Question 8

A sign test is a test of hypothesis about the population mean.

Question 9

The Wilcoxon signed ranks test is also called the Mann-Whitney test.

Question 10

The Wilcoxon rank sum test is a nonparametric test used to compare the central tendencies of two populations when a paired difference experiment has been conducted.

Question 11

The sign test is a nonparametric test for a population mean that is valid for any sample size and population shape.

Question 12

The Wilcoxon signed ranks test is a nonparametric test.

Question 13

Which one of the following nonparametric methods can be used with a single population?

A) Spearman's test
B) sign test
C) Kruskal-Wallis test
D) Wilcoxon rank sum test

Question 14

Which one of the following nonparametric methods requires that we carry out a paired difference experiment?

A) Wilcoxon signed ranks test
B) sign test
C) Kruskal-Wallis test
D) Wilcoxon rank sum test

Question 15

The Kruskal-Wallis test requires that all p samples being compared must have equal sample sizes.

Question 16

In testing the significance of a population correlation coefficient using the Spearman's rank correlation coefficient,it is assumed that all possible combinations of values of variable X and variable Y have a bivariate normal probability distribution.

Question 17

An assumption of the Wilcoxon rank sum test is that the variances of the two populations are equal.

Question 18

The Spearman's rank correlation test can be used to study the relationship between two ordinal variables.

Question 19

The Wilcoxon rank sum test and the Kruskal-Wallis test both require that we take independent random samples.

Question 20

The Wilcoxon rank sum test requires that two independent samples being compared must have equal sample sizes.

Question 21

Refer to the MegaStat/Excel output for the Wilcoxon rank sum test given in the table below. At a significance level of .05,which one of the following statements is correct regarding the following null hypothesis? H₀: D₁ and D₂ are identical probability distributions.

A) We reject H₀ and conclude there is very strong evidence that the median value of the first sample significantly differs from the median value of the second sample.
B) We reject H₀ and conclude there is very strong evidence that the median value of the first sample is significantly less than the median value of the second sample.
C) We do not reject H₀ and conclude there is not sufficient evidence that the median value of the first sample is significantly less than the median value of the second sample.
D) We do not reject H₀ and conclude there is insufficient evidence to conclude that the median value of the first sample is not significantly different from the median value of the second sample.
E) We do not reject H₀ and conclude there is very strong evidence that the median value of the first sample is significantly greater than the median value of the second sample.

Question 22

Which one of the following nonparametric methods can be considered as an extension of the Wilcoxon rank sum test?

A) Wilcoxon signed ranks test
B) sign test
C) Kruskal-Wallis test
D) Spearman's test

Question 23

Assume that the following data set is not normally distributed.(21,18,4,9,14,16,17,12,15,8,7,5) If H_a: M_d > 6,then the p value is

A) .0161.
B) .0029.
C) .0537.
D) .0322.
E) .0192.

Question 24

Which one of the following nonparametric methods can be used to determine the strength of the relationship between two variables?

A) Wilcoxon signed ranks test
B) sign test
C) Kruskal-Wallis test
D) Wilcoxon rank sum test
E) Spearman's test

Question 25

Parametric methods are ____________ more powerful than their nonparametric counterparts.

A) always
B) sometimes
C) never

Question 26

The signed ranks test is the nonparametric counterpart of the

A) small-sample t test about a single population mean.
B) two independent samples t test.
C) one-way ANOVA F test.
D) paired difference t test.
E) F test for equality of population variances.

Question 27

The Wilcoxon signed ranks test is the nonparametric counterpart of the

A) large sample test about a single population mean.
B) two independent samples t test.
C) one-way ANOVA F test.
D) paired difference t test.
E) F test for equality of population variances.

Question 28

A cholesterol test was given to 10 heart patients with high cholesterol levels.The same 10 heart patients are then given a new cholesterol-reducing drug for six months.Before the patients begin taking the drug,they are told to maintain their current diets and eating habits so that the effect of the drug can be more effectively determined.After taking the drug for six months,the same patients are given a cholesterol test again.The pharmaceutical company manufacturing the medicine wants to know if the drug is effective in reducing the cholesterol levels of the patients.The cholesterol levels before and after taking the drug are recorded for each patient.The population of cholesterol levels is not normally distributed.Which one of the following nonparametric tests is appropriate for this problem?

A) Wilcoxon signed ranks test
B) Wilcoxon rank sum test
C) sign test
D) Kruskal-Wallis test
E) Spearman's rank correlation test

Question 29

Refer to the MegaStat/Excel output for the Wilcoxon rank sum test given in the table below. At a significance level of .05,which one of the following rejection point conditions is correct regarding the following null hypothesis? H₀: D₁ and D₂ are identical probability distributions.

A) Reject H₀ if T ≥ 79 or T ≤ 131.
B) Reject H₀ if T ≥ 131 or T ≤ 83.
C) Reject H₀ if T ≥ 131 or T ≤ 79.
D) Reject H₀ if T ≤ 83 or T ≥ 127.
E) Reject H₀ if T ≤ 79 or T ≥ 127.

Question 30

Assume that the following data set is not normally distributed.(21,18,4,9,14,16,17,12,15,8,7,5) If H_a: M_d < 16,then the p value is

A) .1208.
B) .1937.
C) .0537.
D) .3874.
E) .1458.

Question 31

The Wilcoxon rank sum test is the nonparametric counterpart of the

A) large-sample test about a single population mean.
B) two independent samples t test.
C) F test.
D) paired-difference t test.
E) F test for equality of population variances.

Question 32

The EPA has stipulated that the Pollution Standard Index (PSI)for clean air standards is to average no more than 100.A random sample of 9 days for the city of Acorn showed PSI readings of 144,85,90,120,150,105,93,130,and 115.Assume the population of PSI readings is highly nonnormal.The EPA wants to determine if there is significant evidence to conclude that Acorn's air is dirtier than the stipulated clean air standards.Which one of the following tests is appropriate for this problem?

A) Wilcoxon signed ranks test
B) Wilcoxon rank sum test
C) sign test
D) Kruskal-Wallis test
E) Spearman's rank correlation test

Question 33

Refer to the MegaStat/Excel output for the Wilcoxon rank sum test given in the table below. At a significance level of .05,which one of the following rejection point conditions is correct regarding the null hypothesis,H₀: D₁ and D₂ are identical probability distributions,and the alternative hypothesis of H_a: D₁ is shifted to the left of D₂

A) Reject H₀ if T ≥ 83.
B) Reject H₀ if T ≤ 127.
C) Reject H₀ if T ≥ 131.
D) Reject H₀ if T ≤ 83.
E) Reject H₀ if T ≤ 79.

Question 34

The Kruskal-Wallis test is the nonparametric counterpart of the

A) large-sample test about a single population mean.
B) two independent samples t test.
C) one-way ANOVA F test.
D) paired-difference t test.
E) F test for equality of population variances.

Question 35

An e-business/e-commerce information technology consulting company wants to compare the effectiveness of three programming languages that its programmers use.Currently each programming language is used by approximately 1/3 of the programmers employed by the company.The director of the programming division randomly selected 5 programmers from the users of each of the three programming languages and assigned the same simple programming task to each programmer.It is known that all three populations have highly skewed distributions with extreme outliers.Which one of the following nonparametric tests is appropriate for this problem?

A) Wilcoxon signed ranks test
B) Wilcoxon rank sum test
C) sign test
D) Kruskal-Wallis test
E) Spearman's rank correlation test

Question 36

Assume that the following data set is not normally distributed.(21,18,4,9,14,16,17,12,15,8,7,5) If H_a: M_d ≠ 7,then the p value is

A) .0161.
B) .0029.
C) .1458.
D) .0729.
E) .0537.

Question 37

Two NFL scouts are in the process of recruiting seven college senior football players (receivers).After a careful review and evaluation,both scouts ranked the seven receivers in terms of their professional career prospects.If we want to determine whether the two scouts have similar opinions about the professional football career prospects of the seven players,which one of the following non parametric tests would we choose?

A) Wilcoxon signed ranks test
B) Wilcoxon rank sum test
C) sign test
D) Kruskal-Wallis test
E) Spearman's rank correlation test

Question 38

In a manufacturing facility producing fasteners,a foreman suspects that the diameter of the bolts produced by his second-shift workers is greater than the diameter of the bolts produced by his first-shift workers.He takes a sample of five bolts from the first shift and a sample of four bolts from the second shift and measures the diameters in inches.The population of bolt diameter measurements is not normally distributed.Which one of the following nonparametric tests is appropriate for this problem?

A) Wilcoxon signed ranks test
B) Wilcoxon rank sum test
C) sign test
D) Kruskal-Wallis test
E) Spearman's rank correlation test

Question 39

Refer to the MegaStat/Excel output for the Wilcoxon rank sum test given in the table below. At a significance level of .05,which one of the following rejection point conditions is correct regarding the null hypothesis,H₀: D₁ and D₂ are identical probability distributions,and the alternative hypothesis of H_a: D₁ is shifted to the left of D₂.

A) We reject H₀ and conclude that there is very strong evidence that the median value of the first sample significantly differs from the median value of the second sample.
B) We reject H₀ and conclude that there is very strong evidence that the median value of the first sample is significantly less than the median value of the second sample.
C) We do not reject H₀ and conclude there is not sufficient evidence that the median value of the first sample is significantly less than the median value of the second sample.
D) We do not reject H₀ and conclude there is not sufficient evidence to conclude that the median value of the first sample is not significantly different than the median value of the second sample.
E) We do not reject H₀ and conclude there is very strong evidence that the median value of the first sample is significantly less than the median value of the second sample.

Question 40

Five years ago,the average starting salary of a new college graduate with a major in marketing was $34,000.A random sample of 10 graduates from this year's graduating class of a local university yielded the following starting salaries in thousands of dollars: 38,36,25,37,35,24,38,45,39,36.The local university wants to determine if the starting salaries have increased in the last five years.Assume that the population of starting salaries in marketing is not normally distributed.Which one of the following tests is appropriate for this problem?

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

Question 41

In order to perform the ________________ ,all of the observations in two samples are combined into a single set and all of the values in the single set are ranked from smallest to largest.

A) Wilcoxon rank sum test
B) Kruskal-Wallis H test
C) Wilcoxon signed ranks test
D) sign test

Question 42

Refer to the MegaStat/Excel output for the Wilcoxon signed ranks test given in the table below. At a significance level of .01,which one of the following rejection point conditions is correct regarding the null hypothesis,H₀: D₁ and D₂ are identical probability distributions,and the alternative hypothesis of H_a: D₁ is shifted to the left of D₂.

A) T⁻ ≤ 2
B) T⁺ ≤ 2
C) T⁻ ≤ 0
D) T⁻ ≤ 6
E) The smaller of T⁺ or T⁻ is less than 8.

Question 43

In a Wilcoxon rank sum test,when two or more observations are equal,we assign to each tied observation a rank equal to the _________ of the consecutive ranks.

A) average
B) median
C) sum
D) difference

Question 44

The Kruskal-Wallis H statistic can be approximated by the _____________ distribution.

A) normal
B) chi-square
C) z
D) t

Question 45

Wax-com Electronics Inc.claims that a certain circuit board has a median operating life of less than 20,000 hours.A random sample of 25 such circuit boards showed 8 circuit boards failing before 20,000 hours and 17 circuit boards failing after 20,000 hours.Assume the useful life of the circuit board is not normally distributed and state the null hypothesis.

A) H₀: M_d ≥ 20,000
B) H₀: M_d ≤ 20,000
C) H₀: M_d < 20,000
D) H₀: M_d ≠ 20,000

Question 46

The __________________ is a nonparametric counterpart of a one-way ANOVA F test.

A) Wilcoxon rank sum test
B) Kruskal-Wallis H test
C) Wilcoxon signed ranks test
D) sign test

Question 47

When a large sample is taken,the _______________ approximation to the binomial distribution can be used to implement the sign test.

A) chi-square
B) normal
C) correlation coefficient
D) rank sum

Question 48

Refer to the MegaStat/Excel output for the Wilcoxon signed ranks test given in the table below. At a significance level of .01,which one of the following rejection point conditions is correct regarding the null hypothesis,H₀: D₁ and D₂ are identical probability distributions,and the alternative hypothesis of H_a: D₁ is shifted to the left of D₂.

A) We reject H₀ and conclude there is not sufficient evidence that the probability distribution of population 1 is shifted to the left of the probability distribution of population 2.
B) We cannot reject H₀ and conclude there is not sufficient evidence that the probability distribution of population 1 is shifted to the left of the probability distribution of population 2.
C) We reject H₀ and conclude there is very strong evidence that the probability distribution of population 1 is shifted to the left of the probability distribution of population 2.
D) We do not reject H₀ and conclude there is very strong evidence that the probability distribution of population 1 is shifted to the left or to the right of the probability distribution of population 2.
E) We do not reject H₀ and conclude there is very strong evidence that the probability distribution of population 1 is identical to the probability distribution of population 2.

Question 49

The ______________ is a nonparametric method that requires data consisting of matched pairs.

A) Wilcoxon rank sum test
B) Kruskal-Wallis test
C) Wilcoxon signed ranks test
D) sign test

Question 50

A cholesterol test was given to ten heart patients with high cholesterol levels.The same ten heart patients are then given a new cholesterol-reducing drug for six months.Before the patients begin taking the drug,they are told to maintain their current diets and eating habits so that the effect of the drug can be more effectively determined.After taking the drug for six months,the same patients are given a cholesterol test again.The cholesterol levels before and after taking the drug are given below.The cholesterol level readings are not normally distributed.At α = .05,test to determine if the drug is helpful in reducing cholesterol levels.Cholesterol level Patient

A) Reject the null hypothesis.
B) Do not reject the null hypothesis.

Question 51

A professional organization is attempting to determine whether salaries of hospital CFOs differ by geographical region.Five hospital CFOs were randomly selected from each of the following four regions of the United States: East,Midwest,South,and West.Each CFO was then asked his or her annual salary.The salary distributions were highly skewed.The table below summarizes the results of the Kruskal-Wallis test obtained from MegaStat/Excel. At a significance level of .05,which one of the following statements is correct regarding the following null hypothesis? H₀: The four populations under consideration have identical salaries.

A) We reject H₀ and conclude that there is very strong evidence that the median hospital CFO salaries differ among all four regions in the United States.
B) We failed to reject H₀ and conclude that there is not sufficient evidence that the median hospital CFO salaries differ among any of the four regions of the United States.
C) We do not reject H₀ and conclude that there is only adequate evidence that the median hospital CFO salaries differ between at least two of the four regions in the United States.
D) We reject H₀ and conclude that there is strong evidence that the median hospital CFO salaries differ between at least two of the four regions in the United States.
E) We do not reject H₀ and conclude that all 4 populations under consideration are identical in their locations.

Question 52

In a local ice skating contest,there were 2 judges and 15 contestants.Each judge was asked to rate each contestant on a 7-point scale.The most successful candidates received a rating value of 7,while the least successful candidates received a rating value of 1.It appears that the bivariate normal probability distribution assumption was severely violated.The City Council wants to know whether the judges have similar opinions in rating ice skating competitors.At a significance level of .01,the rejection point condition for the hypothesis test is

A) reject H₀ if r_s > .457.
B) reject H₀ if r_s > .623.
C) reject H₀ if r_s > .441.
D) reject H₀ if r_s > .646.
E) reject H₀ if r_s > .689.

Question 53

The __________________ is a nonparametric counterpart of a small-sample t test for comparing two independent population locations.

A) Wilcoxon rank sum test
B) Kruskal-Wallis H test
C) Wilcoxon signed ranks test
D) sign test

Question 54

A professional organization is attempting to determine whether salaries of hospital CFOs differ by geographical region.Five hospital CFOs were randomly selected from each of the following four regions of the United States: East,Midwest,South,and West.Each CFO was then asked his or her annual salary.The salary distributions were highly skewed.The table below summarizes the results of the Kruskal-Wallis test obtained from MegaStat/Excel. At a significance level of .05,the rejection point condition for the hypothesis test is

A) reject H₀ if χ² > 9.3484.
B) reject H₀ if χ² > 30.1435.
C) reject H₀ if χ² > 7.81473.
D) reject H₀ if χ² > .341846.
E) reject H₀ if χ² > 32.8523.

Question 55

An e-business/e-commerce information technology consulting company wants to compare the effectiveness of three programming languages that its programmers use.Currently each programming language is used by approximately 1/3 of the company's programmers.The director of the programming division randomly selected 5 programmers from the users of each of the three programming languages and assigned the same simple programming task to each programmer.All three populations have highly skewed distributions with extreme outliers.The rank sum values for each of the programming groups are T₁ = 23,T₂ = 48,and T₃ = 49.At α = .05,does the median time required to program a simple task differ between the three different programming languages?

A) H = 4.34,reject the null hypothesis.
B) H = 4.34,do not reject the null hypothesis.
C) H = 5.99,reject the null hypothesis.
D) H = 5.99,do not reject the null hypothesis.

Question 56

If the population from which we sample is highly skewed to the right or to the left,then the population _________ might be a better measure of central tendency than the population mean.

A) median
B) variance
C) mode
D) average

Question 57

A cholesterol test was given to ten heart patients with high cholesterol levels.The same ten heart patients are then given a new cholesterol-reducing drug for six months.Before the patients begin taking the drug,they are told to maintain their current diets and eating habits so that the effect of the drug can be more effectively determined.After taking the drug for six months,the same patients are given a cholesterol test again.The pharmaceutical company that manufactures the drug wants to determine if the drug is helpful in reducing cholesterol levels.The cholesterol level readings are not normally distributed.State the alternative hypothesis for this problem.

A) The probability distribution of cholesterol readings of patients before and after the trials is identical.
B) The probability distribution of cholesterol readings at the end of six months has shifted to the left of the probability distribution of cholesterol readings at the beginning of the trials.
C) The probability distribution of cholesterol readings at the end of six months has shifted to the right of the probability distribution of cholesterol readings at the beginning of the trials.
D) The probability distribution of cholesterol readings of patients at the end of six months has shifted to the right or left of the probability distribution of cholesterol readings at the beginning of the trials.

Question 58

In order to perform the ________________,all of the observations in p samples are combined into a single set and all of the values in the single set are ranked from smallest to largest.After ranking,the sum of the ranks for each of the p samples is calculated.

A) Wilcoxon rank sum test
B) Kruskal-Wallis H test
C) Wilcoxon signed ranks test
D) sign test

Question 59

A ___________ can be used without assuming that the sampled population(s)has/have a particular type of probability distribution.

A) t- test
B) nonparametric test
C) linear regression test
D) correlation test

Question 60

The Wilcoxon rank sum test is used to compare the locations of two _____________ populations.

A) dependent
B) normal
C) independent
D) similar

Question 61

Two NFL scouts are in the process of recruiting seven college senior football players (receivers).After a careful review and evaluation,both scouts ranked the seven receivers in terms of their professional career prospects.If we want to determine whether the two scouts have similar opinions about the professional football career prospects of the seven players,state the null hypothesis.

A) H₀: ρ_s ≠ 0
B) H₀: ρ_s ≥ 0
C) H₀: ρ_s ≤ 0
D) H₀: ρ_s = 0