Question 1

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 Wilcoxon Signed-Rank test in order to determine whether or not the seminar has been effective. Hint: This is a one tailed test. Let $\alpha$ = 0.05.

Accepted Answer

The answer of The following data show the test scores...

Question 2

For the Wilcoxon signed-rank test, differences of 0 are
A)discarded
B)assigned a rank of n/2
C)assigned a rank of n
D)assigned a rank of n + 1

Accepted Answer

Differences of 0 are discarded in the Wilcoxon signed-rank test because they do not contribute to the test's assessment of whether the median difference between paired observations is zero.

Question 3

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 $\alpha$ = 0.05, test for a significant difference in the preference for the candidates.

Accepted Answer

The answer of The following data show the preference of...

Question 4

Exhibit 18-6
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 HS1U1B10S1U1B0: median = $70,000.
-Refer to Exhibit 18-6. To test the null hypothesis, the appropriate probability distribution to use is
A)normal
B)chi-square
C)t distribution
D)binomial

Accepted Answer

The answer of Exhibit 18-6
It is believed that the median...

Question 5

Ten drivers were asked to drive two models of a car. Each car was given one gallon of gasoline. The distance that each automobile traveled on a gallon of gasoline is shown below.  
At $\alpha$ = 0.05, what can be concluded about the performance of the two models?

Accepted Answer

The answer of Ten drivers were asked to drive two...

Question 6

Exhibit 18-6
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 HS1U1B10S1U1B0: median = $70,000.
-Refer to Exhibit 18-6. The p-value for this test is
A)0.4332
B)0.8664
C)0.0668
D)0.1336

Accepted Answer

The p-value is calculated using the binomial test for the median. With 38 incomes above $70,000 and 26 below, the test statistic is based on the number of incomes above the median. The p-value is approximately 0.1336.

Question 7

In a sample of 300 shoppers, 160 indicated they prefer fluoride toothpaste, 120 favored nonfluoride, and 20 were indifferent. At a 0.05 level of significance, test for a difference in the preference for the two kinds of toothpaste.

Accepted Answer

The answer of In a sample of 300 shoppers, 160...

Question 8

Exhibit 18-6
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 HS1U1B10S1U1B0: median = $70,000.
-Refer to Exhibit 18-6. The null hypothesis should be
A)rejected
B)not rejected
C)revised
D)None of these alternatives is correct.

Accepted Answer

The null hypothesis states that the median income is $70,000. Since 38 residents have income above $70,000, and only 26 below, it suggests that the median income is actually higher than $70,000. However, this difference may be due to chance. Therefore, we need to conduct a hypothesis test to see if there is sufficient evidence to reject the null hypothesis. Based on the given data, we cannot reject the null hypothesis at any reasonable level of significance. Thus, the null hypothesis should not be rejected.

Question 9

Exhibit 18-6
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 HS1U1B10S1U1B0: median = $70,000.
-Refer to Exhibit 18-6. The test statistic has a value of
A)1.00
B)1.50
C)2.00
D)2.50

Accepted Answer

The test statistic is calculated as (38 - 26) / sqrt(67 * 0.5 * 0.5) = 1.50.

Question 10

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 0.05 level of significance, determine if there is evidence of a significant difference in the preferences for the two makes of automobiles.

Accepted Answer

The answer of In a sample of 120 people, 50...

Question 11

If the assumption can be made that the populations all have the same shape, the Kruskal-Wallis test becomes
A)a test of the skewness of the k populations
B)a test of the variances of the k populations
C)a test of the medians of the k populations
D)a test of the means of the k populations

Accepted Answer

If the populations all have the same shape, then the Kruskal-Wallis test becomes a test of the medians of the k populations. This is because the Kruskal-Wallis test is a non-parametric test that ranks the data and compares the medians of the groups. It does not assume normality or equal variances, but rather tests whether the samples come from the same distribution in terms of the center. Therefore, the best choice is C, a test of the medians of the k populations.

Question 12

Two employers (A and B) ranked five candidates for a new position. Their rankings of the candidates are shown below.  
Compute the Spearman rank-correlation and test it for significance. Let $\alpha$ = 0.05.

Accepted Answer

The answer of Two employers (A and B) ranked five...

Question 13

Ten administrative assistants were sent to take a typing efficiency course. The following data show the typing speeds of the administrative assistants before and after the course.  
At $\alpha$ = 0.05, what can be concluded about the effectiveness of the course?

Accepted Answer

The answer of Ten administrative assistants were sent to take...

Question 14

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 husband and wives. Let $\alpha$ = 0.05

Accepted Answer

The answer of From the courthouse records, it is found...

Question 15

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

Accepted Answer

Ties among absolute differences are assigned the average of their ranks in the Wilcoxon signed-rank test. This maintains the integrity of the data and prevents ties from unfairly affecting the analysis.

Question 16

Fifteen people were asked to indicate their preference for domestic versus imported cars. The following data showed their preferences.  
With $\alpha$ = 0.06, test for a significant difference in the preferences for cars. A "+" indicates a preference for imported cars.

Accepted Answer

The answer of Fifteen people were asked to indicate their...

Question 17

Nonparametric methods which can be used to make inferences about a population without requiring an assumption about the distribution of the population are called
A)continuity-correction methods
B)non-probabilistic methods
C)distribution-free methods
D)non-quantitative methods

Accepted Answer

Nonparametric methods are distribution-free methods, which means they do not make assumptions about the shape or form of the underlying population distribution. Therefore, the best choice is C, distribution-free methods. A is incorrect because continuity correction is a method used to adjust the boundaries of the distribution when approximating a continuous distribution with a discrete one. B is incorrect because non-probabilistic methods do not rely on probability theory, but this does not necessarily mean that they are distribution-free. D is incorrect because non-quantitative methods refer to methods that do not involve measurements or numerical values, which is not the case for nonparametric methods.

Question 18

Independent random samples of ten day students and ten evening students at a university showed the following age distributions.  
Use $\alpha$ = 0.05 and test for any significant differences in the age distribution of the two populations.

Accepted Answer

The answer of Independent random samples of ten day students...

Question 19

Exhibit 18-6
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 HS1U1B10S1U1B0: median = $70,000.
-Refer to Exhibit 18-6. 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

Accepted Answer

The answer of Exhibit 18-6
It is believed that the median...

Question 20

The sales records of two branches of a department store over the last 12 months are shown below. (Sales figures are in thousands of dollars.)  
Use $\alpha$ = 0.05 and test to determine if there is a significant difference in the populations of the sales of the two branches.

Accepted Answer

The answer of The sales records of two branches of...

Quiz 18: Nonparametric Methods

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 Wilcoxon Signed-Rank test in order to determine whether or not the seminar has been effective. Hint: This is a one tailed test. Let α\alphaα = 0.05.

For the Wilcoxon signed-rank test, differences of 0 are

Ten drivers were asked to drive two models of a car. Each car was given one gallon of gasoline. The distance that each automobile traveled on a gallon of gasoline is shown below. At α\alphaα = 0.05, what can be concluded about the performance of the two models?

In a sample of 300 shoppers, 160 indicated they prefer fluoride toothpaste, 120 favored nonfluoride, and 20 were indifferent. At a 0.05 level of significance, test for a difference in the preference for the two kinds of toothpaste.

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

Two employers (A and B) ranked five candidates for a new position. Their rankings of the candidates are shown below. Compute the Spearman rank-correlation and test it for significance. Let α\alphaα = 0.05.

Ten administrative assistants were sent to take a typing efficiency course. The following data show the typing speeds of the administrative assistants before and after the course. At α\alphaα = 0.05, what can be concluded about the effectiveness of the course?

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 husband and wives. Let α\alphaα = 0.05

For the Wilcoxon signed-rank test, ties among absolute differences are assigned the

Fifteen people were asked to indicate their preference for domestic versus imported cars. The following data showed their preferences. With α\alphaα = 0.06, test for a significant difference in the preferences for cars. A "+" indicates a preference for imported cars.

Nonparametric methods which can be used to make inferences about a population without requiring an assumption about the distribution of the population are called

Independent random samples of ten day students and ten evening students at a university showed the following age distributions. Use α\alphaα = 0.05 and test for any significant differences in the age distribution of the two populations.

The sales records of two branches of a department store over the last 12 months are shown below. (Sales figures are in thousands of dollars.) Use α\alphaα = 0.05 and test to determine if there is a significant difference in the populations of the sales of the two branches.

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 husband and wives. Let $\alpha$ = 0.05