Deck 14: Nonparametric Statistics Available Online

Question 1

Which of the following is unknown, in general?

A)the probability that a randomly selected observation exceeds the median of a normal distribution
B)the probability that a randomly selected observation exceeds the median of a nonnormal distribution
C)the probability that a randomly selected observation exceeds the mean of a nonnormal distribution
D)the probability that a randomly selected observation exceeds the mean of a normal distribution

Answer 1

C

Question 2

What are distribution-free tests?

Answer 2

Distribution-free tests are statistical tests that do not rely on any underlying
assumptions about the probability distribution of the sampled population.

Question 3

Answer 3

Question 4

Eight SmartCars were randomly selected and the highway mileage of each was noted. The highway mileage per gallon for each car is shown below:

Question 5

Question 6

The sign test provides inferences about the population median rather than the population mean.

Question 7

Fifteen SmartCars were randomly selected and the highway mileage of each was noted. It was desired to determine if the median miles per gallon of all SmartCars exceeded 35 miles per gallon.
What type of nonparametric analysis should be used?

Question 8

Question 9

Nonparametric methods focus on the location of the probability distribution, rather than on
specific parameters of the population.

Question 10

Question 11

The only assumption necessary to ensure the validity of the sign test is that the probability
distribution of measurements is continuous.

Question 12

If a distribution is approximately normal, the t-test is a more powerful test about the central
tendency of the distribution than the sign test.

Question 13

For a sign test to be valid, a large sample must be selected from a population which is
approximately normal.

Question 14

What are rank statistics (or rank tests)?

Question 15

A convenience store owner believes that the median number of lottery tickets sold per day
is 47. A random sample of 20 days yields the data below. Test the ownerʹs claim. Use α =
.05.

Question 16

Nonparametric tests are useful for qualitative data that can be ranked.

Question 17

What is referred to as nonparametrics?

Question 18

The sign test can not be used when an outlier is present.

Question 19

The median household income of a community is reported to be $62,000. A random
sample of six households in the community yielded the following incomes.

Question 20

Eight SmartCars were randomly selected and the highway mileage of each was noted. The highway mileage per gallon for each car is shown below:

Question 21

When performing a rank test comparing two populations, we rank the sample observations from
both populations as though they were drawn from the same population.

Question 22

At six different randomly chosen times, a researcher measures the temperature (in degrees
Fahrenheit)of a pint of milk from a supermarketʹs shelf. The measurements are shown
below.

Question 23

The Wilcoxon rank sum test is recommended for comparing discrete distributions.

Question 24

Specify the rejection region for the Wilcoxon rank sum test in the following situation.

Question 25

Online classes are becoming more and more prevalent at the college level. A statistics instructor randomly sampled ten students from his traditional face-to-face class and ten students from his
Online class to compare their comprehension of the material that was taught in the class. He
Administered the same final exam to each student and wants to use the Wilcoxon Rank Sum test to
Compare their exam scores. The results are shown below: Calculate the test statistic for the Wilcoxon Rank Sum Test for Large Samples.

A)z = -0.756
B)z = 0.756
C)z = 115
D)z = 95

Question 26

The results of independent random samples from two populations are shown below. Calculate the rank sum for each sample. Which would be used as the test statistic in a
Wilcoxon rank sum test?

Question 27

The Wilcoxon rank sum test is used to test the hypothesis that the probability distributions
associated with two populations are equivalent.

Question 28

Online classes are becoming more and more prevalent at the college level. A statistics instructor randomly sampled ten students from his traditional face-to-face class and ten students from his
Online class to compare their comprehension of the material that was taught in the class. He
Administered the same final exam to each student and wants to use the Wilcoxon Rank Sum test to
Compare their exam scores. The results are shown below:

Question 29

For the Wilcoxon rank sum test to be valid, the number of ties in the measurements needs to be
small relative to the sample sizes.

Question 30

Question 31

Question 32

Question 33

Online classes are becoming more and more prevalent at the college level. A statistics instructor randomly sampled ten students from his traditional face-to-face class and ten students from his
Online class to compare their comprehension of the material that was taught in the class. He
Administered the same final exam to each student and wants to use the Wilcoxon Rank Sum test to
Compare their exam scores. The results are shown below: What alternative hypothesis should the instructor test to show that the students in the traditional
Class outperformed the students in the online class?

A)The distribution of exams scores for the traditional class is shifted to the right of the distribution of exams scores for the online class.
B)The distribution of exams scores for the traditional class is shifted to the left of the distribution of exams scores for the online class.
C)The distribution of exams scores for the traditional class is shifted to the right or to the left of the distribution of exams scores for the online class.
D)The distribution of exams scores for the traditional class is identical to the distribution of exams scores for the online class.

Question 34

The results of independent random samples from two populations are shown below. Calculate the rank sum for each sample. Which would be used as the test statistic in a
Wilcoxon rank sum test?

Question 35

Suppose you want to compare two treatments, A and B. In particular, you wish to
determine whether the distribution for population B is shifted to the right of the
distribution for population A. You plan to use the Wilcoxon rank sum test. Sample A: 1.2, 1.5, 2.3, 3.2, 3.7, 4.1
Sample B: 2.5, 2.8, 3.6, 4.2, 4.5

Question 36

Independent random samples from two populations are shown in the table.

Question 37

A government agency claims that the median hourly wages for workers at fast food
restaurants in the western U.S. is $8.20. In a random sample of 100 workers, 68 were paid
less than $8.20, 10 were paid $8.20, and the rest more than $8.20. Test the governmentʹs
claim.

Question 38

Specify the rejection region for the Wilcoxon rank sum test in the following situation.

Question 39

A marketing study was conducted to compare the mean age of male and female purchasers of a certain product. Random and independent samples were selected for both male and female
Purchasers of the product. It was desired to test to determine if the distribution of ages of all
Female purchasers was shifted to the right of the distribution of ages of all male purchasers. What
Type of nonparametric analysis should be used?

Question 40

Test the hypothesis that the median age of statistics teachers is 46 years. A random sample
of 60 statistics teachers found 25 above 46 years and 35 below 46 years.

Question 41

Specify the rejection region for the Wilcoxon signed rank test in the following situation.

Question 42

Question 43

Question 44

Do popular diets really help customers in the long-run? Many diets help customers lose weight initially only to have the customer add the weight back on after the first few months on the diet. A
Commercially successful diet company conducted a study of twelve randomly selected customers
And measured their weight after before starting the diet and then again after staying with the diet
For a year. The company hoped that the initial weight loss would be sustained after the first year on
The diet. The data is shown below:

Question 45

Do popular diets really help customers in the long-run? Many diets help customers lose weight initially only to have the customer add the weight back on after the first few months on the diet. A
Commercially successful diet company conducted a study of twelve randomly selected customers
And measured their weight after before starting the diet and then again after staying with the diet
For a year. The company hoped that the initial weight loss would be sustained after the first year on
The diet. The data is shown below:

Question 46

Question 47

Question 48

When performing a signed rank test in a paired difference experiment, tied absolute value
differences are assigned the average of the ranks they would receive if they were unequal, but
successive measurements.

Question 49

A scientist is hoping to compare the levels of DDT toxin found in three species of fish in a local river. He randomly samples 7 of each species to use in the analysis. For each fish, he measures the
Amount of DDT toxin present. The data is shown below:

Question 50

Question 51

For a valid signed rank test, the probability distribution from which the sample of paired
differences is drawn must be continuous.

Question 52

When applying the Wilcoxon signed rank test, the number of ties should be small relative to the
number of observations to ensure the validity of the test.

Question 53

For a valid Kruskal-Wallis test, the probability distribution from which the samples are drawn
must be continuous.

Question 54

A scientist is hoping to compare the levels of DDT toxin found in three species of fish in a local river. He randomly samples 50 of each species to use in the analysis. For each fish, he measures the
Amount of DDT toxin present. Ideally he will be able to determine if a difference exists in the
Population of DDT toxins found in the three fish species. What type of nonparametric analysis
Should be used?

Question 55

Do popular diets really help customers in the long-run? Many diets help customers lose weight initially only to have the customer add the weight back on after the first few months on the diet. A
Commercially successful diet company conducted a study of twelve randomly selected customers
And measured their weight after before starting the diet and then again after staying with the diet
For a year. The company hoped that the initial weight loss would be sustained after the first year on
The diet. The data is shown below:

Question 56

Question 57

Specify the rejection region for the Wilcoxon signed rank test in the following situation.

Question 58

A certain manufacturer is interested in evaluating two alternative manufacturing plans consisting of different machine layouts. Because of union rules, hours of operation vary greatly for this
Particular manufacturer from one day to the next. Twenty-eight random working days were
Selected and each plan was monitored and the number of items produced each day was recorded.
Some of the collected data is shown below:

Question 59

The Kruskal-Wallis test is valid only when each sample contains five or fewer measurements.

Question 60

The Wilcoxon signed rank test for large samples can be used when n ≥ 10.

Question 61

Four brands of baseball bats were tested to determine which bat allowed hitters to hit a baseball farthest. Eight different batters were thrown 25 pitches while hitting with each of the four bats
(assigned in random order). The median distance of the five longest hits using each bat is shown in
The table below. The goal is to determine if a difference exists in the population of median
Distances for each of the four brands of baseball bat.

Question 62

Question 63

A realtor wishes to compare the square footage of houses in 4 different cities, all of which
are priced approximately the same. The data are listed below. Use the Kruskal-Wallis test
to test the claim that there is no difference in the distribution of the populations. Use

Question 64

Question 65

Four different types of fertilizers are used on raspberry plants. The number of raspberries
on each randomly selected plant is given below. Use the Kruskal-Wallis H-test to test the
claim that there is no difference in the distribution of the populations.

Question 66

Consider the data set shown below. Find the Spearmanʹs Rank Correlation for the variables x and y.

Question 67

Question 68

Question 69

When there is a perfect negative rank correlation between two variables, the value of the test

Question 70

Question 71

Four brands of baseball bats were tested to determine which bat allowed hitters to hit a baseball farthest. Eight different batters were thrown 25 pitches while hitting with each of the four bats
(assigned in random order). The median distance of the five longest hits using each bat is shown in
The table below. The goal is to determine if a difference exists in the population of median
Distances for each of the four brands of baseball bat.

Question 72

Is there evidence that at least two of the treatment probability distributions differ in
location? Explain.

Question 73

A scientist is hoping to compare the levels of DDT toxin found in three species of fish in a local river. He randomly samples 7 of each species to use in the analysis. For each fish, he measures the
Amount of DDT toxin present. The data is shown below:

Question 74

Question 75

A scientist is hoping to compare the levels of DDT toxin found in three species of fish in a local river. He randomly samples 7 of each species to use in the analysis. For each fish, he measures the
Amount of DDT toxin present. The data is shown below:

Question 76

Four brands of baseball bats were tested to determine which bat allowed hitters to hit a baseball farthest. Eight different batters were thrown 25 pitches while hitting with each of the four bats
(assigned in random order). The median distance of the five longest hits using each bat is shown in
The table below. The goal is to determine if a difference exists in the population of median
Distances for each of the four brands of baseball bat.

Question 77

Question 78

For a valid Spearmanʹs test, the probability distribution for just one of the two variables must be
continuous.

Question 79

Question 80

The time (in minutes)it takes to assemble a computer component for three different
machines is listed below. Workers are randomly selected. Use the Kruskal-Wallis test to
test the claim that there is no difference in the distribution of the populations.