Deck 20: Nonparametric Tests

Question 1

When conducting a hypothesis test for the ________ m, we want to determine whether m is not equal to, greater than, or less than m₀, the value of the population median postulated in the null hypothesis.

Answer 1

population median

Question 2

If the distributional assumptions of a parametric test are valid yet we choose to use a nonparametric test, the nonparametric test is more powerful.

Answer 2

False

Question 3

If we have a matched-pairs sample of ordinal data, we can use the sign test to determine whether there are significant differences between the ________.

Answer 3

populations

Question 4

The Kruskal-Wallis test is always a ________-tailed test.

Question 5

If we wish to compare central tendencies from nonnormal populations, then the Wilcoxon signed-rank test serves as the nonparametric counterpart to the ________ test.

Question 6

The Wilcoxon rank-sum test is used as a nonparametric counterpart to the matched-pairs t test.

Question 7

Parametric tests typically assume the underlying population to be normally distributed.

Question 8

Parametric tests are distribution-free tests.

Question 9

The null hypothesis of the Wald-Wolfowitz runs test is the elements do not occur randomly.

Question 10

The Wilcoxon signed-rank test for a population median does not assume anything about the distribution of the population.

Question 11

The Kruskal-Wallis test is a nonparametric alternative to the ________ test that can be used when the assumptions of normality and/or equal population variances cannot be validated.

Question 12

Pearson's correlation coefficient is used as the nonparametric counterpart to the regular correlation coefficient.

Question 13

In the Wald-Wolfowitz test a ________ is an uninterrupted sequence of one letter, symbol, or attribute.

Question 14

The sign test for a matched-pairs sample is similar to the Wilcoxon signed-rank test but applied to ordinal data.

Question 15

Nonparametric tests do not require data of interval or ratio scale.

Question 16

Nonparametric tests use fewer and weaker ________ than those associated with parametric tests.

Question 17

The Kruskal-Wallis test is the nonparametric alternative to one-way ANOVA.

Question 18

The Wilcoxon rank-sum test is based completely on the ________ of the observations from the two independent samples.

Question 19

The method of runs above and below the median is especially useful in detecting trends and cyclical patterns in ________ data.

Question 20

For the Spearman rank correlation test we can use the normal distribution approximation to implement a z test only if n is greater or equal to ________.

Question 21

For the Kruskal-Wallis test with n_i ≥ 5, the sampling distribution of the test statistic, H, can be approximated by the ________.

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

Question 22

The nonparametric test for two population medians under independent sampling is known as ________.

A) Wilcoxon signed-rank test
B) Wilcoxon rank-sum test
C) Kruskal-Wallis test
D) Wald-Wolfowitz runs test

Question 23

For the Wald-Wolfowitz runs test with n₁ ≥ 10 and n₂ ≥ 10, the sampling distribution of the test statistic R can be approximated by the normal distribution with mean of ________.

A) μ_R = - 1
B) μ_R = + 1
C) μ_R =
D) μ_R = + 1

Question 24

For the Wald-Wolfowitz runs test with n₁ ≥ 10 and n₂ ≥ 10, the sampling distribution of the test statistic R can be approximated by the normal distribution with standard deviation ________.

A) σ_R =
B) σ_R =
C) σ_R =
D) σ_R =

Question 25

The nonparametric test for a single population median is known as the ________.

A) Wilcoxon signed-rank test
B) Wilcoxon rank-sum test
C) Kruskal-Wallis test
D) Wald-Wolfowitz runs test

Question 26

For the Wilcoxon rank-sum test when the sample sizes are at least 10, the sampling distribution of the test statistic can be approximated by the normal distribution with standard deviation ________.

A) σ_W =
B) σ_W =
C) σ_W =
D) σ_W =

Question 27

A pawn shop claims to sell used Kindles for about the same price as Amazon or eBay. Both online retailers sell used Kindles for around $150. Below are recent Kindle sales prices for the pawn shop. Which of the following is the value of the test statistic?

A) 6
B) 14
C) 20
D) 1

Question 28

The nonparametric test for ordinal data based on matched-pairs sampling is the ________.

A) Wilcoxon signed-rank test
B) Wald-Wolfowitz runs test
C) the sign test
D) Spearman's rank correlation test

Question 29

For the Wilcoxon signed-rank test with n ≥ 10, the sampling distribution of the test statistic can be approximated by the normal distribution with mean ________.

A) μ_T = 2n(2n + 1)/2
B) μ_T = n(n + 1)/4
C) μ_T = n(n - 1)/4
D) μ_T = n(2n + 1)/3

Question 30

The nonparametric test for the correlation between two variables is known as the ________.

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

Question 31

Which of the following is the test statistic for the Kruskal-Wallis test?

A) H = - 3(n + 1)
B) H = - 3(n + 1)
C) H = - 3(n + 1)
D) H = + 3(n + 1)

Question 32

For the Wilcoxon rank-sum test when the sample sizes are at least 10, the sampling distribution of the test statistic can be approximated by the normal distribution with mean ________.

A) μ_W =
B) μ_W =
C) μ_W =
D) μ_W =

Question 33

The nonparametric test to determine if a sequence is random is ________.

A) Wilcoxon signed-rank test
B) Wald-Wolfowitz runs test
C) the sign test
D) Spearman's rank correlation test

Question 34

Which of the following is the test statistic for the sign test?

A) z =
B) z =
C) z =
D) z =

Question 35

Which of the following is the sample Spearman rank correlation coefficient?

A) r_s = 1 -
B) r_s = 1 -
C) r_s = 1 -
D) r_s = 1 -

Question 36

A pawn shop claims to sell used Kindles for about the same price as Amazon or eBay. Both online retailers sell used Kindles for around $150. Below are recent Kindle sales prices for the pawn shop. At the 5% significance level, the critical value is ________.

A) 2
B) 19
C) 0
D) 28

Question 37

For the Wilcoxon signed-rank test with n ≥ 10, the sampling distribution of the test statistic can be approximated by the normal distribution with standard deviation ________.

A) σ_T =
B) σ_T =
C) σ_T =
D) σ_T =

Question 38

If n ≥ 10, the sampling distribution of the Spearman rank correlation coefficient can be approximated by the normal distribution with ________.

A) µ = 0 and σ =
B) µ = 1 and σ =
C) µ = 0 and σ =
D) µ = 0 and σ =

Question 39

The test statistic for the sign test is = where ________.

A) is the sample proportion of plus signs
B) is the sample proportion of minus signs
C) is the sample mean of plus signs
D) is the sample mean of minus signs

Question 40

A pawn shop claims to sell used Kindles for about the same price as Amazon or eBay. Both online retailers sell used Kindles for around $150. Below are recent Kindle sales prices for the pawn shop. Which of the following are the competing hypotheses to determine if the median sale price is greater than $150?

A) H₀: m ≤ 150; H_A: m > 150
B) H₀: m ≥ 150; H_A: m < 150
C) H₀: m ≠ 150; H_A: m = 150
D) H₀: m = 150; H_A: m ≠ 150

Question 41

Investment institutions usually have funds with different risk versus reward prospectuses. A trading magazine wants to determine if the returns of high-risk funds are greater than low-risk funds. The magazine records the return of high- and low-risk funds for a sample of 22 institutions. For the Wilcoxon signed-rank test, where D = high-risk return − low-risk return, the value of the test statistic is T = T⁺ = 185. Given the sample size, the sampling distribution of T can be approximated by the normal distribution as the sample size is greater than 10; T can be assumed to follow the normal distribution with mean and standard deviation ________, respectively.

A) 126.5 and 30.80
B) 30.80 and 126.5
C) 125.5 and 948.75
D) 30.80 and 984.75

Question 42

A pawn shop claims to sell used Kindles for about the same price as Amazon or eBay. Both online retailers sell used Kindles for around $150. Below are recent Kindle sales prices for the pawn shop. The p-value for the test is ________.

A) less than 0.01
B) between 0.025 and 0.01
C) between 0.05 and 0.025
D) greater than 0.05

Question 43

A company that produces financial accounting software wants to offer better training to its customers. The training is intended to decrease the amount of time required to do complicated accounting calculations. For seven individuals, the amount of time (in minutes) to complete a complicated calculation is determined before and after completing the new training. Using the p-value approach and α = 0.05, the appropriate conclusion is ________.

A) do not reject the null hypothesis; we cannot conclude the median difference of the times is greater than zero
B) do not reject the null hypothesis; we can conclude the median difference of the times is greater than zero
C) reject the null hypothesis; we cannot conclude the median difference of the times is greater than zero
D) reject the null hypothesis; we can conclude the median difference of the times is greater than zero

Question 44

A trading magazine wants to determine the number of hours stockbrokers work each week. In particular, the trading magazine wants to determine if the median number of hours worked per week differs from 100 hours. The magazine samples 18 traders. For the Wilcoxon signed-rank test, the value of the test statistic is T = T⁺ = 153. The p-value for the test is ________.

A) 0.0016
B) 0.0032
C) 0.9984
D) 0

Question 45

A company that produces financial accounting software wants to offer better training to its customers. The training is intended to decrease the amount of time required to do complicated accounting calculations. For seven individuals, the amount of time (in minutes) to complete a complicated calculation is determined before and after completing the new training. For the Wilcoxon signed-rank test for the matched-pairs sample, the competing hypotheses are ________.

A) H₀: m_D ≤ 0; H_A: m_D > 0
B) H₀: m_D = 0; H_A: m_D ≠ 0
C) H₀: m_D ≠ 0; H_A: m_D = 0
D) H₀: m_D ≥ 0; H_A: m_D < 0

Question 46

A pawn shop claims to sell used Kindles for about the same price as Amazon or eBay. Both online retailers sell used Kindles for around $150. Below are recent Kindle sales prices for the pawn shop. Using the p-value approach and α = 0.05, the appropriate conclusion is ________.

A) to reject the null hypothesis; we cannot conclude the median sale price is greater than $150
B) do not reject the null hypothesis; we cannot conclude the median sale price is greater than $150
C) do not reject the null hypothesis; we can conclude the median sale price is greater than $150
D) to reject the null hypothesis; we can conclude the median sale price is greater than $150

Question 47

A trading magazine wants to determine the number of hours stockbrokers work each week. In particular, the trading magazine wants to determine if the median numbers worked per week differs from 100 hours. The magazine samples 18 traders. For the Wilcoxon signed-rank test, the value of the test statistic is T = T⁺ = 153. Given the sample size, the sampling distribution of T can be approximated by the normal distribution with mean and standard deviation ________, respectively.

A) 85.50, 527.25
B) 22.96, 527.25
C) 22.96, 85.50
D) 85.50, 22.96

Question 48

Investment institutions usually have funds with different risk versus reward prospectuses. A trading magazine wants to determine if the returns of high-risk funds is greater than low-risk funds. The magazine records the return of high- and low-risk funds for a sample of 22 institutions. For the Wilcoxon signed-rank test, where D = high-risk return − low-risk return, the value of the test statistic is T = T⁺ = 185. At the 10% significance level, the critical value is ________.

A) 1.645
B) 1.96
C) 2.33
D) 2.575

Question 49

A company that produces financial accounting software wants to offer better training to its customers. The training is intended to decrease the amount of time required to do complicated accounting calculations. For seven individuals, the amount of time (in minutes) to complete a complicated calculation is determined before and after completing the new training. Using the critical value approach and α = 0.05, the appropriate conclusion is ________.

A) reject the null hypothesis; we cannot conclude the median difference of the times is greater than zero
B) reject the null hypothesis; we can conclude the median difference of the times is greater than zero
C) do not reject the null hypothesis; we cannot conclude the median difference of the times is greater than zero
D) do not reject the null hypothesis; we can conclude the median difference of the times is greater than zero

Question 50

Investment institutions usually have funds with different risk versus reward prospectuses. A trading magazine wants to determine if the returns of high-risk funds are greater than low-risk funds. The magazine records the return of high- and low-risk funds for a sample of 22 institutions. For the Wilcoxon signed-rank test, where D = high-risk return − low-risk return, the value of the test statistic is T = T⁺ = 185. For the Wilcoxon signed-rank test for the matched-pairs, the competing hypotheses are ________.

A) H₀: m_D = 0; H_A: m_D ≠ 0
B) H₀: m_D ≤ 0; H_A: m_D > 0
C) H₀: m_D ≠ 0; H_A: m_D = 0
D) H₀: m_D ≥ 0; H_A: m_D < 0

Question 51

A trading magazine wants to determine the number of hours stockbrokers work each week. In particular, the trading magazine wants to determine if the median number of hours worked per week differs from 100 hours. The magazine samples 18 traders. For the Wilcoxon signed-rank test, the value of the test statistic is T = T⁺ = 153. Using the critical value approach and α = 0.01, the appropriate conclusion is ________.

A) to reject the null hypothesis; we cannot conclude the median number of hours worked per week differs from 100
B) do not reject the null hypothesis; we can conclude the median number of hours worked per week differs from 100
C) do not reject the null hypothesis; we cannot conclude the median number of hours worked per week differs from 100
D) to reject the null hypothesis; we can conclude the median number of hours worked per week differs from 100

Question 52

A trading magazine wants to determine the number of hours stockbrokers work each week. In particular, the trading magazine wants to determine if the median number of hours worked per week differs from 100 hours. The magazine samples 18 traders. For the Wilcoxon signed-rank test, the value of the test statistic is T = T⁺ = 153. If the sampling distribution of T can be approximated by the normal distribution, the value of the z test statistic is ________.

A) 153
B) 2.94
C) 0.128
D) −2.94

Question 53

A company that produces financial accounting software wants to offer better training to its customers. The training is intended to decrease the amount of time required to do complicated accounting calculations. For seven individuals, the amount of time (in minutes) to complete a complicated calculation is determined before and after completing the new training. At the 5% significance level, the critical value is ________.

A) 25
B) 3
C) 2
D) 26

Question 54

A company that produces financial accounting software wants to offer better training to its customers. The training is intended to decrease the amount of time required to do complicated accounting calculations. For seven individuals, the amount of time (in minutes) to complete a complicated calculation is determined before and after completing the new training. The p-value for the test is ________.

A) less than 0.01
B) between 0.01 and 0.025
C) between 0.025 and 0.05
D) greater than 0.05

Question 55

A company that produces financial accounting software wants to offer better training to its customers. The training is intended to decrease the amount of time required to do complicated accounting calculations. For seven individuals, the amount of time (in minutes) to complete a complicated calculation is determined before and after completing the new training. The value of the test statistic is ________.

A) 5
B) 23
C) 7
D) 13

Question 56

A pawn shop claims to sell used Kindles for about the same price as Amazon or eBay. Both online retailers sell used Kindles for around $150. Below are recent Kindle sales prices for the pawn shop. Using the critical value approach and α = 0.05, the appropriate conclusion is ________.

A) to reject the null hypothesis; conclude the median sale price is greater than $150
B) do not reject the null hypothesis; we cannot conclude the median sale price is greater than $150
C) to reject the null hypothesis; we cannot conclude the median sale price is greater than $150
D) do not reject the null hypothesis; conclude the median sale price is greater than $150

Question 57

A trading magazine wants to determine the number of hours stockbrokers work each week. In particular, the trading magazine wants to determine if the median numbers worked per week differs from 100 hours. The magazine samples 18 traders. For the Wilcoxon signed-rank test, the value of the test statistic is T = T⁺ = 153. Which of the following are the competing hypotheses to determine if the median number of hours worked per week differs from 100 hours?

A) H₀: m ≤ 100; H_A: m > 100
B) H₀: m ≥ 100; H_A: m < 100
C) H₀: m ≠ 100; H_A: m = 100
D) H₀: m = 100; H_A: m ≠ 100

Question 58

Investment institutions usually have funds with different risk versus reward prospectuses. A trading magazine wants to determine if the returns of high-risk funds are greater than low-risk funds. The magazine records the return of high- and low-risk funds for a sample of 22 institutions. For the Wilcoxon signed-rank test, where D = high-risk return − low-risk return, the value of the test statistic is T = T⁺ = 185. Assuming that the sampling distribution of T can be approximated by the normal distribution, the value of the z test statistic is ________.

A) 0.062
B) 22
C) 185
D) 1.899

Question 59

A trading magazine wants to determine the number of hours stockbrokers work each week. In particular, the trading magazine wants to determine if the median number of hours worked per week differs from 100 hours. The magazine samples 18 traders. For the Wilcoxon signed-rank test, the value of the test statistic is T = T⁺ = 153. Using the p-value approach and α = 0.01, the appropriate conclusion is ________.

A) to reject the null hypothesis; we can conclude the median number of hours worked per week differs from 100
B) to reject the null hypothesis; we cannot conclude the median number of hours worked per week differs from 100
C) do not reject the null hypothesis; we can conclude the median number of hours worked per week differs from 100
D) do not reject the null hypothesis; we cannot conclude the median number of hours worked per week differs from 100

Question 60

A trading magazine wants to determine the number of hours stockbrokers work each week. In particular, the trading magazine wants to determine if the median number of hours worked per week differs from 100 hours. The magazine samples 18 traders. For the Wilcoxon signed-rank test, the value of the test statistic is T = T⁺ = 153. At the 1% significance level, the critical value is ________.

A) 1.645
B) 1.96
C) 2.33
D) 2.575

Question 61

A fund manager wants to know if the annual rate of return is greater for growth stocks (sample 1) than for value stocks (sample 2). The fund manager collects data on the returns of growth and value funds. Below are the sample sizes and rank sums for the Wilcoxon rank-sum test. The p-value for the test is ________.

A) greater than 0.10
B) between 0.10 and 0.05
C) between 0.05 and 0.01
D) less than 0.01

Question 62

Investment institutions usually have funds with different risk versus reward prospectuses. A trading magazine wants to determine if the returns of high-risk funds is greater than low-risk funds. The magazine records the return of high- and low-risk funds for a sample of 22 institutions. For the Wilcoxon signed-rank test, where D = high-risk return − low-risk return, the value of the test statistic is T = T⁺ = 185. Using the critical value approach and α = 0.10, the appropriate conclusion is ________.

A) to reject the null hypothesis; we cannot conclude the median difference of the returns is greater than zero
B) do not reject the null hypothesis; we cannot conclude the median difference of the returns is greater than zero
C) to reject the null hypothesis; we can conclude the median difference of the returns is greater than zero
D) do not reject the null hypothesis; we can conclude the median difference of the returns is greater than zero

Question 63

An accountant wants to know if the property taxes paid by clients who live in the city are different from those who live in the county. The property taxes paid by five clients from the city (sample 1) and five clients from the county (sample 2) are shown below. To determine whether the medians of the taxes paid differ using the Wilcoxon rank-sum test, the competing hypotheses are ________.

A) H₀: m₁ - m₂ ≥ 0; H_A: m₁ - m₂ < 0
B) H₀: m₁ - m₂ ≤ 0; H_A: m₁ - m₂ > 0
C) H₀: m₁ - m₂ ≠ 0; H_A: m₁ - m₂ = 0
D) H₀: m₁ - m₂ = 0; H_A: m₁ - m₂ ≠ 0

Question 64

Investment institutions usually have funds with different risk versus reward prospectuses. A trading magazine wants to determine if the returns of high-risk funds is greater than low-risk funds. The magazine records the return of high- and low-risk funds for a sample of 22 institutions. For the Wilcoxon signed-rank test, where D = high-risk return − low-risk return, the value of the test statistic is T = T⁺ = 185. Using the p-value approach and α = 0.10, the appropriate conclusion is ________.

A) to reject the null hypothesis; we can conclude the median difference of the returns is greater than zero
B) to reject the null hypothesis; we cannot conclude the median difference of the returns is greater than zero
C) do not reject the null hypothesis; we cannot conclude the median difference of the returns is greater than zero
D) do not reject the null hypothesis; we can conclude the median difference of the returns is greater than zero

Question 65

An accountant wants to know if the property taxes paid by clients who live in the city are different from those who live in the county. The property taxes paid by five clients from the city (sample 1) and five clients from the county (sample 2) are shown below. At the 5% significance level, the critical values are ________.

A) 18 and 37
B) 19 and 36
C) 18 and 36
D) 19 and 37

Question 66

A marketing firm needs to replace its existing network provider and is considering three different providers. A primary consideration is the amount of system downtime. The following table contains the amount of network downtime (in hours) for the last five months for each network provider. The p-value for the test is ________.

A) less than 0.01
B) between 0.01 and 0.05
C) between 0.05 and 0.10
D) greater than 0.10

Question 67

A fund manager wants to know if the annual rate of return is greater for growth stocks (sample 1) than for value stocks (sample 2). The fund manager collects data on the returns of growth and value funds. Below are the sample sizes and rank sums for the Wilcoxon rank-sum test. The value of the test statistic W is ________.

A) 215
B) 9,870
C) 13,350
D) 23,200

Question 68

Investment institutions usually have funds with different risk versus reward prospectuses. A trading magazine wants to determine if the returns of high-risk funds is greater than low-risk funds. The magazine records the return of high- and low-risk funds for a sample of 22 institutions. For the Wilcoxon signed-rank test, where D = high-risk return − low-risk return, the value of the test statistic is T = T⁺ = 185. The p-value for the test is ________.

A) greater than 0.10
B) between 0.10 and 0.05
C) between 0.05 and 0.01
D) less than 0.01

Question 69

A marketing firm needs to replace its existing network provider and is considering three different providers. A primary consideration is the amount of system downtime. The following table contains the amount of network downtime (in hours) for the last five months for each network provider. At the 5% significance level, the critical value is ________.

A) 4.605
B) 5.991
C) 7.378
D) 9.21

Question 70

An accountant wants to know if the property taxes paid by clients who live in the city are different from those who live in the county. The property taxes paid by five clients from the city (sample 1) and five clients from the county (sample 2) are shown below. The value of the test statistic is ________.

A) 10
B) 21
C) 34
D) 55

Question 71

An accountant wants to know if the property taxes paid by clients who live in the city are different from those who live in the country. The property taxes paid by five clients from the city (sample 1) and five clients from the country (sample 2) are shown below. Using the critical value approach and α = 0.05, the appropriate conclusion is ________.

A) reject the null hypothesis; we cannot conclude the median taxes paid in the city differs from the median taxes paid in the country
B) do not reject the null hypothesis; conclude the median taxes paid in the city differs from the median taxes paid in the country
C) reject the null hypothesis; we can conclude the median taxes paid in the city differs from the median taxes paid in the country
D) do not reject the null hypothesis; we cannot conclude the median taxes paid in the city differs from the median taxes paid in the country

Question 72

A fund manager wants to know if the annual rate of return is greater for growth stocks (sample 1) than for value stocks (sample 2). The fund manager collects data on the returns of growth and value funds. Below are the sample sizes and rank sums for the Wilcoxon rank-sum test. To determine whether the median return of growth funds is larger than the median return of value funds, the competing hypotheses are ________.

A) H₀: m₁ - m₂ ≥ 0; H_A: m₁ - m₂ < 0
B) H₀: m₁ - m₂ ≤ 0; H_A: m₁ - m₂ > 0
C) H₀: m₁ - m₂ ≠ 0; H_A: m₁ - m₂ = 0
D) H₀: m₁ - m₂ = 0; H_A: m₁ - m₂ ≠ 0

Question 73

A marketing firm needs to replace its existing network provider and is considering three different providers. A primary consideration is the amount of system downtime. The following table contains the amount of network downtime (in hours) for the last five months for each network provider. Using the critical value approach and α = 0.05, the appropriate conclusion is ________.

A) reject the null hypothesis, we cannot conclude not all median network downtimes are equal
B) do not reject the null hypothesis, we cannot conclude not all median network downtimes are equal
C) reject the null hypothesis, we can conclude not all median network downtimes are equal
D) do not reject the null hypothesis, we can conclude not all median network downtimes are equal

Question 74

A marketing firm needs to replace its existing network provider and is considering three different providers. A primary consideration is the amount of system downtime. The following table contains the amount of network downtime (in hours) for the last five months for each network provider. For the Kruskal-Wallis test, the competing hypotheses are ________.

A) H₀: m_A = m_B = m_C; H_A: Not all population medians are equal
B) H₀: m_A = m_B = m_C; H_A: m_A ≠ m_C
C) H₀: m_A = m_B = m_C; H_A: m_A ≠ m_B
D) H₀: m_A = m_B = m_C; H_A: m_B ≠ m_C

Question 75

A marketing firm needs to replace its existing network provider and is considering three different providers. A primary consideration is the amount of system downtime. The following table contains the amount of network downtime (in hours) for the last five months for each network provider. The test statistic value is ________.

A) 7.8
B) 13.0
C) 3.2
D) 12.02

Question 76

A fund manager wants to know if the annual rate of return is greater for growth stocks (sample 1) than for value stocks (sample 2). The fund manager collects data on the returns of growth and value funds. Below are the sample sizes and rank sums for the Wilcoxon rank-sum test. Using the critical value approach and α = 0.01, the appropriate conclusion is ________.

A) reject the null hypothesis; we can conclude the median return of growth stocks is greater than the median return of value stocks
B) do not reject the null hypothesis; we cannot conclude the median return of growth stocks is greater than the median return of value stocks
C) do not reject the null hypothesis; we can conclude the median return of growth stocks is greater than the median return of value stocks
D) reject the null hypothesis; we cannot conclude the median return of growth stocks is greater than the median return of value stocks

Question 77

A fund manager wants to know if the annual rate of return is greater for growth stocks (sample 1) than for value stocks (sample 2). The fund manager collects data on the returns of growth and value funds. Below are the sample sizes and rank sums for the Wilcoxon rank-sum test. Using the p-value approach and α = 0.01, the appropriate conclusion is ________.

A) do not reject the null hypothesis; conclude the median return of growth stock is greater than the median return of value
B) do not reject the null hypothesis; we cannot conclude the median return of growth stock differs from the median return of value stocks
C) reject the null hypothesis; conclude the median return of growth stock is greater than the median return of value stocks
D) reject the null hypothesis; we cannot conclude the median return of growth stock is greater than the median return of value stocks

Question 78

A fund manager wants to know if the annual rate of return is greater for growth stocks (sample 1) than for value stocks (sample 2). The fund manager collects data on the returns of growth and value funds. Below are the sample sizes and rank sums for the Wilcoxon rank-sum test. Because both sample sizes are at least 10, the sampling distribution of W can be approximated by the normal distribution with a mean and standard deviation of ________, respectively.

A) 434.74 and 8100
B) 8100 and 434.74
C) 8100 and 189000
D) 189000 and 8100

Question 79

A fund manager wants to know if the annual rate of return is greater for growth stocks (sample 1) than for value stocks (sample 2). The fund manager collects data on the returns of growth and value funds. Below are the sample sizes and rank sums for the Wilcoxon rank-sum test. Assuming that the sampling distribution of W can be approximated by the normal distribution, the value of the test statistic is ________.

A) 4.07
B) −4.07
C) −12.07
D) 12.07

Question 80

A fund manager wants to know if the annual rate of return is greater for growth stocks (sample 1) than for value stocks (sample 2). The fund manager collects data on the returns of growth and value funds. Below are the sample sizes and rank sums for the Wilcoxon rank-sum test. At the 1% significance level, the critical value is ________.

A) 1.645
B) 1.96
C) 2.33
D) 2.575