Deck 13: Nonparametric Statistics

Question 1

What is another term for nonparametric statistics?

A)distribution-free statistics
B)inferential statistics
C)parametric tests
D)sign test

Answer 1

distribution-free statistics

Question 2

Nonparametric methods use less information than their parametric counterparts.

Answer 2

True

Question 3

If two judges were asked to rank 10 science fair projects, the Spearman rank correlation coefficient would
be 0.70 given that the sum of squares is equal to 50.

Answer 3

True

Question 4

Since the Wilcoxon rank sum test uses only the ranks of the data values and not the actual magnitudes of
the data values, it is never as powerful as the corresponding t-test.

Question 5

What is the term that refers to any statistical test, such as the z-, t-, or F-test?

A)distribution-free statistics
B)nonparametric statistics
C)parametric test
D)sign test

Question 6

The test for randomness considers the frequency of the letters rather than the number of runs.

Question 7

Given the following data, what is the ranking of data point 15? 16, 18, 12, 19, 15, 20, 13, 18

A)3
B)4
C)5
D)6

Question 8

The Kruskal-Wallis test is always left-tailed.

Question 9

Nonparametric statistics can be applied to populations when the assumption of normality cannot be
met.

Question 10

The Wilcoxon rank sum test is used to test dependent samples, and the Wilcoxon signed-rank test is used
for independent samples.

Question 11

If a researcher wanted to prove that there is a relationship between two variables and had collected
30 data points for each group, the Spearman rank correlation coefficient could be used, but Pearson's
correlation coefficient would be a better choice for a test method.

Question 12

Given that a variable is normally distributed, researchers will need more data to determine the same
information using parametric methods than they would for nonparametric methods.In other words,
parametric methods are not as efficient as nonparametric methods.

Question 13

A run is a succession of identical letters preceded or followed by a different letter or no letter at all, such
as the beginning or end of the succession.

Question 14

The smaller number of + or - signs is used in the z Test static in the Sign Test for samples of 26 or
bigger

Question 15

In order to determine whether two variables are linearly related for non-normally distributed data, one
uses the Spearman rank correlation coefficient.

Question 16

When using the Kruskal-Wallis test to compare three or more means, it is necessary to consider all data
values together and then rank them.

Question 17

If data is normally distributed, then the Wilcoxon signed-rank test is more powerful than the t-test.

Question 18

The sign test does not consider the magnitude of the data.

Question 19

Nonparametric methods are more sensitive than their parametric counterparts when the assumptions of
the parametric methods are met.

Question 20

If data is normally distributed, then the Wilcoxon signed-rank test is more powerful than the sign test.

Question 21

Given the following data, what is the ranking of data point 27? 30, 30, 20, 33, 37, 32, 15, 27

A)2
B)3
C)4
D)5

Question 22

A researcher believes that the median amount of rain per year is 36 inches.A random sample of 20 years yields the following data: At = .05, should the researcher's hypothesis be accepted or rejected?
You may use the following abbreviated table of critical values (two tailed, = .05) taken from Table
J:

A)Reject because the test value 6 is more than the critical value 6
B)Do not reject because the test value 7 is more than the critical value 6
C)Reject because the test value 6 is more than the critical value 5
D)Do not reject because the test value 7 is more than the critical value 5

Question 23

If a researcher is using the sign test and has 12 positive signs and 7 negative signs, then the test value is:

A)7
B)5
C)-5
D)12

Question 24

Given the following data, what is the ranking of data point 24? 27, 24, 17, 30, 34, 29, 12, 24

A)2
B)2.5
C)3
D)3.5

Question 25

It was thought that hypnosis would lower a person's need to smoke.A researcher decided to investigate this hypothesis using the paired-sample sign test.Given that the critical value for
Ten samples at (single-sided) is 1, is there enough evidence to support the hypothesis?

A)The critical value is less than the test value; therefore, there is not enough evidence to support the hypothesis.
B)The critical value is greater than the test value; therefore, there is not enough evidence to support the hypothesis.
C)The critical value is less than the test value; therefore, there is enough evidence to support the hypothesis.
D)The critical value is greater than the test value; therefore, there is enough evidence to support the hypothesis.

Question 26

A researcher collects data on the distance between college students' high schools and their colleges.He believes that the median distance is 200 miles.A random sample of 15 students yields the following data: At = .05, should the researcher's hypothesis be accepted or rejected?
You may use the following abbreviated table of critical values (two tailed, = .05) taken from Table
J:

A)Reject because the test value 2 is less than the critical value 3
B)Do not reject because the test value 4 is less than the critical value 13
C)Reject because the test value 13 is more than the critical value 3
D)Do not reject because the test value 13 is more than the critical value 3

Question 27

Which of the following is not an advantage of nonparametric methods over parametric methods?

A)They can be used to test population parameters when the variable is not normally distributed.
B)They can be used when the data are nominal or ordinal.
C)They can be used to test hypotheses that do not involve population parameters.
D)They can use smaller sample sizes to give the same amount of information as their parametric counterparts.

Question 28

The data collected for studying whether or not there is a difference between the number of hours men and women watch television is summarized below.To compute the test value, the data from both samples
Should be combined, arranged in order, and ranked according to each group.What is the sum of the ranks
For each group?

A)The sum of the ranks for the men is 162.5, and the sum of the ranks for the woman is 137.5.
B)The sum of the ranks for the men is 170, and the sum of the ranks for the woman is 130.
C)The sum of the ranks for the men is 130, and the sum of the ranks for the woman is 170.
D)The sum of the ranks for the men is 137.5, and the sum of the ranks for the woman is 162.5.

Question 29

It is believed that children can throw a ball farther after lunch than before lunch.A researcher decided to investigate this hypothesis for 14 children using the paired-sample sign test.Each of the distances below
Is in meters. At = .05, do the data support the claim?
You may use the following abbreviated table of critical values (one-tailed, = .05) taken from Table
J:

A)Supports the claim because the test value 4 is more than the critical value 3
B)Does not support the claim because the test value 4 is more than the critical value 3

Question 30

A landscaping company hypothesizes that they can mow a median number of 20 lawns in one weekend.
A random sample of 14 weekends yields the following data:

What is the test value?

A)3
B)4
C)7
D)8

Question 31

A landscaping company hypothesizes that they can mow a median number of 20 lawns in one weekend.
A random sample of 14 weekends yields the following data:

Is the landscaping company's hypothesis of a median of 20 lawns per weekend valid?

A)yes
B)no
C)Null hypothesis is invalid because the numbers of positives and negatives are equal.
D)There are not enough data points to make a valid determination.

Question 32

Given the following data, what is the ranking of data point -31? -28, -28, -38, -25, -21, -26, -43, -31

A)1
B)2
C)3
D)4

Question 33

What is the critical value for the sign test if and there are 14 samples?

A)1
B)2
C)3
D)4

Question 34

Given the following data, what is the ranking of data point 1? 4, 4, -6, 7, 11, 6, -11, 1

A)3
B)4
C)4.5
D)5

Question 35

What type of test takes the magnitude of the data into consideration by using ranks?

A)runs test
B)z-test
C)Wilcoxon rank sum test
D)Kruskal-Wallis test

Question 36

When the sample size is 26 or more, the normal approximation can be used to find the test value when performing the sign test on a sample.The test is now referred to as a:

A)runs test.
B)z-test.
C)Wilcoxon rank sum test.
D)Wilcoxon signed-rank test.

Question 37

A random sample of 12 men and 12 women were asked to report the number of hours they watched television on a Wednesday evening.If a researcher wanted to test the hypothesis that there is no
Difference in the amount of time spent watching television based on gender, what z-values would be used
For the Wilcoxon rank sum test for (two-tailed)?

A)
B)
C)
D)

Question 38

If a researcher were interested in determining whether or not two groups of students received
significantly different grades in statistics, the Wilcoxon rank sum test would be the best method to
use.

Question 39

If a researcher is using the sign test and has 12 positive signs, 18 negative signs, and 4 zeros, what is the test value?

A)0
B)12
C)18
D)None of the above

Question 40

If a researcher is using the sign test and has 13 positive signs and 19 negative signs, then the test value is:

A)19
B)-6
C)6
D)13

Question 41

Two independent samples of tall and short students are selected, and their scores on a 25-point statistics quiz are recorded as shown in the table below.What is the rank of the score for Wilt?

A)10
B)11
C)9
D)8

Question 42

A researcher wished to compare the automobile colour preferences of men and women.An experiment was performed recording the preferences of 10 men and 10 women.If the sum of squares of the ranking
Differences is equal to 8, what is the Spearman Rank Correlation Coefficient ?

A)0.975
B)0.952
C)0.476
D)0.905

Question 43

Use the Kruskal-Wallis test to determine if there is a difference in the means of these five groups. With , and the , the critical value is 9.488.Rank the above data and calculate the
Value for H.Choose the correct table for the summary of the ranking results and the calculation of the H
Value.
Refer To:13-58

A)
B)
C)
D)

Question 44

Six second grade students tried tossing a ball into a basket ten times each.Their teacher then suggested a different way of tossing the ball, and the six students tried again.The
Number of successful tosses, before and after the teacher's added instruction, are shown
Below. Ignoring the differences of 0, the signed rank of child A is:

A)+4
B)+3.5
C)-3
D)-3.5

Question 45

A researcher is interested in investigating two dependent non-normally distributed variables.Which of the following should be used for this application?

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

Question 46

The data collected for studying whether or not there is a difference between the number of hours men and women watch television is summarized below.To compute the test value, the data from both samples
Should be combined, arranged in order, and ranked according to each group.
Calculate the , and z-test value for the Wilcoxon rank sum test started in problem 32 and
Continued in problem 37.

A)
B)
C)
D)

Question 47

Two students were asked to rate six different television shows on a scale from 0 to 10.The data are shown in the following table:
What are the television show rankings for student 2 (to be used to calculate the Spearman Rank
Correlation Coefficient)?

A)A-2, B-1, C-5, D-3.5, E-6, F-3.5
B)A-1, B-5, C-2, D-3.5, E-6, F-3.5
C)A-2, B-1, C-6, D-3.5, E-5, F-3.5
D)A-2, B-1, C-5, D-2.5, E-6, F-2.5

Question 48

Six second grade students tried tossing a ball into a basket ten times each.Their teacher then suggested a different way of tossing the ball, and the six students tried again.The
Number of successful tosses, before and after the teacher's added instruction, are shown
Below.
Ignoring the differences of 0, the positive rank sum is:

A)+9
B)+3
C)-4
D)+1

Question 49

Two independent sets of data are collected, one with 16 subjects and one with 26 subjects.Mr.X is in the first set of data and has a value of 67.In the first set of data, 5 values are higher than 67 and 10 values
Are lower (with Mr.X being the other data value).In the second set, 9 values are higher than 67 and 17
Values are lower.What is the rank of Mr.X?

A)13
B)14
C)27
D)28

Question 50

Two independent sets of data are collected, one with 15 subjects and one with 22 subjects.Ms.X is in the first set of data and has a value of 41.In the first set, 11 values are higher than 41 and 3 values are lower
(with Ms.X being the other data value).In the second set, 16 values are higher than data and 6 values are
Lower.What is the rank of Ms.X?

A)9
B)10
C)26
D)27

Question 51

A researcher tests three different brands of 2% milk to see how many grams of fat are in each 8 ounce glass.The results are shown below. What is the sum of the ranks of Brand A?

A)38.5
B)39.5
C)40.0
D)40.5

Question 52

A researcher is interested in investigating three independent, non-normally distributed variables.Which of the following should be used for this application?

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

Question 53

A researcher tests three different brands of 2% milk to see how many grams of fat are in each 8-ounce glass.The results are shown below. What is the rank of the glass marked "Bessie"?

A)7
B)7.5
C)8.5
D)9

Question 54

A researcher tests three different brands of 2% milk to see how many grams of fat are in each 8 ounce glass.The results are shown below. What is the sum of the ranks of Brand B?

A)27.0
B)29.0
C)32.5
D)35.0

Question 55

Two genetics classes took the same exam and their scores are as shown in the table below.What is the rank of the score for Gregor?

A)8.5
B)9
C)9.5
D)10

Question 56

Six second grade students tried tossing a ball into a basket ten times each.Their teacher then suggested a different way of tossing the ball, and the six students tried again.The
Number of successful tosses, before and after the teacher's added instruction, are shown
Below.
Ignoring the differences of 0, the (unsigned) rank of child C is:

A)4
B)3.5
C)3
D)2.5

Question 57

Two students were asked to rate six different television shows on a scale from 0 to 10.The data are shown in the following table: What are the television show rankings for student 1 (to be used to calculate the Spearman Rank
Correlation Coefficient)?

A)A-1, B-4.5, C-2, D-4.5, E-6, F-3
B)A-2, B-4.5, C-2, D-4.5, E-6, F-2
C)A-1, B-4, C-4, D-5, E-6, F-1
D)A-1, B-4.5, C-2, D-4.5, E-1, F-3

Question 58

When the assumptions for the ANOVA test that populations are normally distributed and population variances are equal cannot be met, the __________ test can be used to compare three or more means.

A)Sign
B)Wilcoxon rank sum
C)z
D)Kruskal-Wallis

Question 59

Six second grade students tried tossing a ball into a basket ten times each.Their teacher then suggested a different way of tossing the ball, and the six students tried again.The
Number of successful tosses, before and after the teacher's added instruction, are shown
Below.
What are the absolute values of the differences?

A)0, 0, 1, 1, 1, 1
B)0, 0, 1, 1
C)1, 1, 2, 2, 3, 3
D)0, 0, 2, 2, 3, 3

Question 60

Six second grade students tried tossing a ball into a basket ten times each.Their teacher then suggested a different way of tossing the ball, and the six students tried again.The
Number of successful tosses, before and after the teacher's added instruction, are shown
Below.
Ignoring the differences of 0, the negative rank sum is:

A)-8
B)+10.5
C)-1
D)-10.5

Question 61

A man wanted to see if the median time to get to work was at least 15 minutes.In a random sample of 40 days, he found that 30 days took more than 15 minutes and the rest took less than 15 minutes.Is there
Enough evidence to support his claim if he uses an =.05?

A)The critical value is less than the test statistic; therefore, there is not enough evidence to support the hypothesis.
B)The critical value is greater than the test statistic; therefore, there is not enough evidence to support the hypothesis.
C)The critical value is less than the test statistic; therefore, there is enough evidence to support the hypothesis.
D)The critical value is greater than the test statistic; therefore, there is enough evidence to support the hypothesis.

Question 62

A pharmaceutical company believes that a new drug should lower blood pressure.In a random sample of 30 test subjects, their blood pressure was measured before taking the drug and then after taking the drug.
It was found that 25 had a lower blood pressure reading after taking the drug while 5 had a higher blood
Pressure reading.Using =.05, is there enough evidence to support the pharmaceutical company?

A)The critical value is less than the test statistic; therefore, there is not enough evidence to support the pharmaceutical company.
B)The critical value is greater than the test statistic; therefore, there is not enough evidence to support the pharmaceutical company.
C)he critical value is less than the test statistic; therefore, there is enough evidence to support the pharmaceutical company.
D)The critical value is greater than the test statistic; therefore, there is enough evidence to support the pharmaceutical company.

Question 63

Test the following sequence for randomness. B A A A A B A B B B B A A A
You may use the following abbreviated table of critical values for runs (at = .05).Reject the null
Hypothesis if the number of runs is less than or equal to the smaller value or greater than or equal to the
Larger value.

A)Do not reject because the test value 6 is not between the critical values 3 and 11
B)Do not reject because the test value 5 is between the critical values 3 and 12
C)Do not reject because the test value 6 is between the critical values 3 and 12
D)Reject because the test value 5 is not between the critical values 3 and 11

Question 64

In the Wilcoxon tests, if the _______________ is true, the values in each sample should be of
approximately the same rank.
________________________________________

Question 65

_______________ are used to test hypotheses that do not involve specific population parameters such as
μ, σ, or r.
________________________________________

Question 66

What is the term for a nonparametric test that is used to determine the randomness of a sample?

A)Sign test
B)Wilcoxon rank sum test
C)runs test
D)Kruskal-Wallis test

Question 67

Many nonparametric tests involve ____________, or positioning of the data values in a data array
according to a scale.
________________________________________

Question 68

How many runs are in the following sequence?

A)5
B)6
C)7
D)8

Question 69

How many runs are in the following sequence?

A)7
B)6
C)5
D)4

Question 70

Two students were asked to rate six different television shows on a scale from 0 to 10.The data are shown in the following table:
What is the Spearman Rank Correlation Coefficient for this set of data?

A)0.432
B)0.559
C)0.725
D)0.886

Question 71

A study of the effects of a chemical additive on soil acidity recorded the soil acidity of eight plots of land before and after the application of the additive.The results
Were: The test value for the sign test is:

A)1
B)2
C)3

Question 72

Test the following sequence for randomness. You may use the following abbreviated table of critical values for runs (at = .05).Reject the null hypothesis if the number of runs is less than or equal to the smaller value or greater than or equal to the
Larger value.

A)Do not reject because the test value 4 is between the critical values 3 and 11
B)Do not reject because the test value 7 is between the critical values 3 and 12
C)Do not reject because the test value 4 is outside the critical values 3 and 11
D)Reject because the test value 7 is between the critical values 3 and 11

Question 73

Two students were asked to rate six different television shows on a scale from 0 to 10.The data are shown in the following table:
What is the sum of squares of the ranking differences (to be used to calculate the Spearman Rank
Correlation Coefficient)?

A)16
B)12
C)8
D)4

Question 74

Two students were asked to rate six different television shows on a scale from 0 to 10.The data are shown in the following table:
What is the Spearman Rank Correlation Coefficient for this set of data?

A)0.413
B)0.536
C)0.694
D)0.886

Question 75

The computations for the rank correlation coefficient for nonparametric data are simpler than those for
the ___________ coefficient and involve ranking each set of data.
________________________________________

Question 76

For a random sample of 40, if 30 values are below the median and 10 are above, compute the test statistic.test.

A)-1.5
B)1.66
C)-3.00
D)3.32

Question 77

Nonparametric tests and statistics can be used in place of their parametric counterparts when the
assumption of ______________ cannot be met.
________________________________________

Question 78

The _______________ is used to test the value of a median for a specific sample.
________________________________________

Question 79

A study of the effects of a chemical additive on soil acidity recorded the acidity of eight plots of land before and after the application of the additive.The results
Were: The test value for the signed-rank test is:

A)1
B)2
C)3
D)4

Question 80

When using nonparametric methods, no knowledge of ______________ is required.
________________________________________