Deck 18: Nonparametric Methods

Question 1

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

A) parametric
B) nonparametric
C) free
D) distribution-fixed

Answer 1

nonparametric

Question 2

The Spearman rank-correlation coefficient for 25 pairs of data when Σd_i² = 50 is

A) .0192.
B) .0376.
C) .9808.
D) .9937.

Answer 2

.9808.

Question 3

A sign test is a

A) nonparametric method for determining the differences between two populations based on two matched samples using the binomial distribution with p = .2 as the sampling distribution.
B) nonparametric method for determining the differences between two populations based on two matched samples using the binomial distribution with p = .5 as the sampling distribution.
C) nonparametric method for determining the differences between two or more populations based on two or more matched samples using the binomial distribution with p = .2 as the sampling distribution.
D) parametric method for determining the differences between two or more populations based on two or more matched samples using the binomial distribution with p = .5 as the sampling distribution.

Answer 3

nonparametric method for determining the differences between two populations based on two matched samples using the binomial distribution with p = .5 as the sampling distribution.

Question 4

The level of measurement that allows for the rank ordering of categorical data items in nonparametric procedures is _____ measurement.

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

Question 5

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 fails to reject the null hypothesis.

Question 6

Nonparametric 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) only deal with computations done on categorical data.

Question 7

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. The p-value for this test is

A) .0005.
B) .001.
C) .0037.
D) .0074.

Question 8

A nonparametric version of the parametric analysis of variance test is the _____ test.

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

Question 9

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 10

When ranking the absolute differences in a Wilcoxon signed-rank test, the value of the difference that receives a rank of 1 is the

A) lowest value.
B) highest value.
C) middle value in the data set.
D) average of the highest and the lowest of values.

Question 11

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

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

Question 12

Students in statistics classes were asked whether they preferred a 10-minute break or to allow them go out of class 10 minutes early. In a sample of 150 students, 40 preferred a 10-minute break, 80 preferred going out 10 minutes early, and 30 had no preference. We want to determine if there is a difference in students' preferences. The null hypothesis that is being tested is

A) H₀: μ = 150.
B) H₀: μ = 75.
C) H₀: p = .2.
D) H₀: p = .5.

Question 13

The level of measurement that is simply a label for the purpose of identifying an item which can be used in nonparametric procedures is _____ measurement.

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

Question 14

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. To test the null hypothesis, the appropriate probability distribution to use is

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

Question 15

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

A) distribution-fixed
B) nonparametric
C) populated
D) parametric

Question 16

Sixteen 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. The null hypothesis that is being tested is

A) H₀: μ = 8.
B) H₀: μ = .5.
C) H₀: p = 8.
D) H₀: p = .5.

Question 17

A nonparametric test would be used if

A) categorical data is available.
B) quantitative data is available.
C) it is known that the population is normally distributed.
D) it is easy to transform categorical data to quantitative data.

Question 18

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. At α = .01, the null hypothesis should

A) be rejected.
B) not be rejected.
C) be revised.
D) not be tested.

Question 19

The Spearman rank-correlation coefficient is a correlation measure based on

A) the average of data items.
B) rank-ordered data for two variables.
C) the median of data items.
D) a linear association between two variables.

Question 20

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 21

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 (in minutes) below. ​ At α = .05, the null hypothesis should

A) be rejected.
B) not be rejected.
C) be revised.
D) not be tested.

Question 22

For the Wilcoxon signed-rank test,

A) ​differences of 0 are​ discarded.
B) ​there are no assumptions made about the population distribution.
C) a skewed population is preferred.
D) ties among absolute differences are assigned positive signed ranks.

Question 23

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 (in minutes) below. ​ The p-value for this test is

A) .3133.
B) .2005.
C) .3734.
D) .8167.

Question 24

Students in statistics classes were asked whether they preferred a 10-minute break or to allow them go out of class 10 minutes early. In a sample of 150 students, 40 preferred a 10-minute break, 80 preferred going out 10 minutes early, and 30 had no preference. We want to determine if there is a difference in students' preferences. The p-value for testing the hypotheses is

A) less than .002.
B) between .002 and .05.
C) between .05 and .10.
D) greater than .10.

Question 25

Students in statistics classes were asked whether they preferred a 10-minute break or to allow them go out of class 10 minutes early. In a sample of 150 students, 40 preferred a 10-minute break, 80 preferred going out 10 minutes early, and 30 had no preference. We want to determine if there is a difference in students' preferences. The mean and the standard deviation, respectively, of the sampling distribution of the number of students who preferred going out early are

A) 50 and 30.
B) 60 and 30.
C) 50 and 5.477.
D) 60 and 5.477.

Question 26

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 (in minutes) below. ​ To test the null hypothesis, the appropriate probability distribution to use is

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

Question 27

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. The test statistic has a value of

A) 1.63.
B) 1.38.
C) 2.00.
D) 2.50.

Question 28

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

A) ​skewness of the k populations.
B) ​variances of the k populations.
C) ​medians of the k populations.
D) ​means of the k populations.

Question 29

It has been hypothesized that there is no difference in the mathematical ability of men and women. To test this hypothesis, decision was taken 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. ​ To test the null hypothesis, the appropriate probability distribution to use is

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

Question 30

It has been hypothesized that there is no difference in the mathematical ability of men and women. To test this hypothesis, decision was taken 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. ​ The null hypothesis is to be tested at the 5% level. The decision rule is to reject the null hypothesis if

A) |z| > 1.96.
B) |t| > 2.08.
C) F > 3.02.
D) χ² > 5.

Question 31

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

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

Question 32

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. At α = .05, the null hypothesis should

A) be rejected.
B) not be rejected.
C) be revised.
D) not be tested.

Question 33

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. To test the null hypothesis, the appropriate probability distribution to use is

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

Question 34

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. The p-value for this test is

A) .4332.
B) .8664.
C) .0838.
D) .1676.

Question 35

It has been hypothesized that there is no difference in the mathematical ability of men and women. To test this hypothesis, decision was taken 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. ​ The mean (μW) is

A) 220.
B) 110.
C) 66.
D) 55.

Question 36

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 (in minutes) below. ​ The test statistic equals

A) -.81 or .81.
B) -.84 or .84.
C) -10 or 10.
D) -20 or 20.

Question 37

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. 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 38

Students in statistics classes were asked whether they preferred a 10-minute break or to allow them go out of class 10 minutes early. In a sample of 150 students, 40 preferred a 10-minute break, 80 preferred going out 10 minutes early, and 30 had no preference. We want to determine if there is a difference in students' preferences. At the 1% level of significance, the null hypothesis should

A) be rejected.
B) not be rejected.
C) be revised.
D) not be tested.

Question 39

Students in statistics classes were asked whether they preferred a 10-minute break or to allow them go out of class 10 minutes early. In a sample of 150 students, 40 preferred a 10-minute break, 80 preferred going out 10 minutes early, and 30 had no preference. We want to determine if there is a difference in students' preferences. The test statistic based on the number of students who preferred going out early equals (Use the continuity correction factor.)

A) 1.83.
B) .67.
C) .82.
D) 3.56.

Question 40

It has been hypothesized that there is no difference in the mathematical ability of men and women. To test this hypothesis, decision was taken 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. ​ The standard deviation (σW) is

A) 34.8.
B) 11.5.
C) 14.2.
D) 110.

Question 41

Fifteen people were asked to indicate their preference for domestic versus imported cars. The following data showed their preferences. ​
With α = .05, test for a significant difference in the preferences for cars. A "+" indicates a preference for imported cars.

Question 42

Two employers (A and B) ranked five candidates for a new position based on their eligibility. Their rankings of the candidates are shown below. ​
Compute the Spearman rank-correlation coefficient.

Question 43

A clothing manufacturer purchased some newly designed sewing machines in the hopes that production would be increased. The production records (in units/week) 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 .10 level of significance.

Question 44

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.
​ ​
Using the Kruskal-Wallis test to determine the mean ranks for each university sampled.

Question 45

Two groups of students were asked to rank the nine activities sponsored by the Student Government Association on campus based on effectiveness. The following table shows their rankings. ​
Determine the Spearman rank-correlation coefficient.

Question 46

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 17 students (6 majoring in accounting, 6 majoring in management, and 5 majoring in marketing). ​
At α = .05, test to see if there is a significant difference in the performance of the students in the three majors.

Question 47

Test scores of ten individuals before and after a training program are shown below. ​
At α = .05, what can be concluded about the effectiveness of the training program?

Question 48

When using the Kruskall-Wallis Test for nonparametric methods, if each sample is at least five, then you can use the _____ distribution for your approximation.

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

Question 49

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 husbands and wives. Let α = .05. Hint: Use the continuity correction factor.

Question 50

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 performance of the students from the three universities. Let α = .05.

Question 51

A survey of male and female students at a university showed the following ranking of 13 professors in the management department based on teaching expertise. ​
Do the rankings given by the female students agree with the rankings given by the male students at the university level? Use α = .05.

Question 52

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 α = .05, test for a significant difference in the preference for the candidates.

Question 53

Two faculty members (X and Y) ranked five candidates for scholarships based on performance in sports and after-school activities. The rankings are shown below. ​
Compute the Spearman rank-correlation coefficient.

Question 54

Two faculty members ranked 13 candidates for scholarships based on overall academic performance. Calculate the Spearman rank-correlation coefficient and test for the significance of the population rank-correlation coefficient. Use a .02 level of significance.

Question 55

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 .05 level of significance, determine if there is evidence of a significant difference in the preferences for the two makes of automobiles. Hint: Use the continuity correction factor.

Question 56

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 α = .05.

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 also called​

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

Question 58

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.