Deck 15: Nonparametric Tests

Question 1

When ranking observation from smallest to largest for use with the Wilcoxon rank sum test and there is a tie,it is best to ___________.

A)assign all tied values the average of the ranks they occupy
B)randomly choose an order for all tied observations
C)assign all tied values the highest rank order possible
D)None of the above

Answer 1

assign all tied values the average of the ranks they occupy

Question 2

Some researchers have conjectured that stem-pitting disease in peach-tree seedlings might be controlled with weed and soil treatment.An experiment was conducted to compare peach-tree seedling growth with soil and weeds treated with one of two herbicides.In a field containing twelve seedlings,six were randomly selected throughout the field and assigned to receive Herbicide A.The remaining six were to receive Herbicide B.Soil and weeds for each seedling were treated with the appropriate herbicide,and at the end of the study period the height in centimeters was recorded for each seedling.The following results were obtained. Let W be the Wilcoxon rank sum test statistic equal to the sum of the ranks assigned to the Herbicide A group.What is the value of z,the standardized value of W?

A)0.37
B)1.76
C)2.24
D)2.32

Answer 2

2.32

Question 3

Does income increase when you get married? To investigate this,a college student has randomly selected people from his college town and collected income data for these people.They were categorized according to their marital status.The following results (in thousands of dollars)were obtained. The data are to be analyzed using the Wilcoxon rank sum test.Let W be the Wilcoxon rank sum test statistic equal to the sum of the ranks assigned to the married group.What is the observed value of W?

A)6
B)21
C)34
D)55

Answer 3

34

Question 4

Does income increase when you get married? To investigate this,a college student has randomly selected people from his college town and collected income data for these people.They were categorized according to their marital status.The following results (in thousands of dollars)were obtained. The data are to be analyzed using the Wilcoxon rank sum test.Arrange the ten observations in order and assign ranks.What rank does the observation with an income of $116,000 receive?

A)3
B)4
C)5
D)7

Question 5

The exact distribution of the Wilcoxon rank sum,W,will not change much in the presence of many tied observations.

Question 6

Some researchers have conjectured that stem-pitting disease in peach-tree seedlings might be controlled with weed and soil treatment.An experiment was conducted to compare peach-tree seedling growth with soil and weeds treated with one of two herbicides.In a field containing twelve seedlings,six were randomly selected throughout the field and assigned to receive Herbicide A.The remaining six were to receive Herbicide B.Soil and weeds for each seedling were treated with the appropriate herbicide,and at the end of the study period the height in centimeters was recorded for each seedling.The following results were obtained. Let W be the Wilcoxon rank sum test statistic equal to the sum of the ranks assigned to the Herbicide A group.What is the expected value of W under the null hypothesis that the two distributions are the same?

A)36
B)39
C)54
D)78

Question 7

Does income increase when you get married? To investigate this,a college student has randomly selected people from his college town and collected income data for these people.They were categorized according to their marital status.The following results (in thousands of dollars)were obtained. The data are to be analyzed using the Wilcoxon rank sum test.Let W be the Wilcoxon rank sum test statistic equal to the sum of the ranks assigned to the married group.What is the standard deviation of W under the null hypothesis that the two distributions are the same?

A)4.56
B)4.79
C)22.9
D)38.67

Question 8

When using the Wilcoxon test and assuming the distribution of the population is not Normal,the null hypothesis would be best stated in terms of the ______.

A)mean
B)median
C)standard deviation
D)variance

Question 9

Does income increase when you get married? To investigate this,a college student has randomly selected people from his college town and collected income data for these people.They were categorized according to their marital status.The following results (in thousands of dollars)were obtained. The data are to be analyzed using the Wilcoxon rank sum test.Let W be the Wilcoxon rank sum test statistic equal to the sum of the ranks assigned to the married group.What is the expected value of W under the null hypothesis that the two distributions are the same?

A)25
B)27.5
C)30
D)55

Question 10

Some researchers have conjectured that stem-pitting disease in peach-tree seedlings might be controlled with weed and soil treatment.An experiment was conducted to compare peach-tree seedling growth with soil and weeds treated with one of two herbicides.In a field containing twelve seedlings,six were randomly selected throughout the field and assigned to receive Herbicide A.The remaining six were to receive Herbicide B.Soil and weeds for each seedling were treated with the appropriate herbicide,and at the end of the study period the height in centimeters was recorded for each seedling.The following results were obtained. When ranking all the observations together,what rank should be assigned to the observations with a height of 77 centimeters?

A)5.0
B)5.5
C)6.0
D)6.5

Question 11

To use nonparametric methods,the distribution of the population should be ________.

A)Normal
B)Binomial
C)Uniform
D)any distribution

Question 12

The distribution of the Wilcoxon rank sum,W,will be closer to a Normal distribution when using the ___________.

A)median
B)binomial correction
C)continuity correction
D)None of the above

Question 13

Does income increase when you get married? To investigate this,a college student has randomly selected people from his college town and collected income data for these people.They were categorized according to their marital status.The following results (in thousands of dollars)were obtained. The data are to be analyzed using the Wilcoxon rank sum test.Let W be the Wilcoxon rank sum test statistic equal to the sum of the ranks assigned to the married group.What is the value of z,the standardized value of W?

A)0.84
B)1.36
C)1.43
D)2.62

Question 14

A researcher has determined that the data obtained in a small study are clearly not Normally distributed.If the researcher had hoped to make inferences based on the data,what might the researcher consider doing in this situation?

A)If the non-Normality is due to the presence of outliers,careful examination may reveal that they are from a different distribution and hence may be removed legitimately.
B)A transformation might be applied to the data to make them more nearly Normal.
C)A nonparametric method such as a rank test based on the rank of each of the observations might be used.
D)A specific distribution other than the Normal might be found,which will serve as an appropriate model for the data.
E)Each of the above might be a possible procedure for the researcher to try.

Question 15

The rank sum statistic,W,is approximately _______ as long as the sample size of both SRSs is large.

A)Normal
B)Binomial
C)Uniform
D)None of the above.

Question 16

Some researchers have conjectured that stem-pitting disease in peach-tree seedlings might be controlled with weed and soil treatment.An experiment was conducted to compare peach-tree seedling growth with soil and weeds treated with one of two herbicides.In a field containing twelve seedlings,six were randomly selected throughout the field and assigned to receive Herbicide A.The remaining six were to receive Herbicide B.Soil and weeds for each seedling were treated with the appropriate herbicide,and at the end of the study period the height in centimeters was recorded for each seedling.The following results were obtained. Let W be the Wilcoxon rank sum test statistic equal to the sum of the ranks assigned to the Herbicide A group.Using the Normal approximation,what is the value of the two-sided P-value for the test?

A)0.0102
B)0.0125
C)0.0203
D)0.0250

Question 17

Which of the following statements about the two-sample Wilcoxon rank sum test is/are FALSE?

A)The samples must each be independent simple random samples.
B)The observations from the combined samples are placed in rank order.
C)The Wilcoxon rank sum statistic is the sum,W,of the ranks for the observations in the first sample.
D)The distribution of W has mean
If the populations are Normally distributed.
E)The hypothesis that the two populations have identical distributions is rejected when the statistic W is far from its mean.

Question 18

Some researchers have conjectured that stem-pitting disease in peach-tree seedlings might be controlled with weed and soil treatment.An experiment was conducted to compare peach-tree seedling growth with soil and weeds treated with one of two herbicides.In a field containing twelve seedlings,six were randomly selected throughout the field and assigned to receive Herbicide A.The remaining six were to receive Herbicide B.Soil and weeds for each seedling were treated with the appropriate herbicide,and at the end of the study period the height in centimeters was recorded for each seedling.The following results were obtained. Let W be the Wilcoxon rank sum test statistic equal to the sum of the ranks assigned to the Herbicide A group.What is the observed value of W?

A)24.5
B)52.0
C)53.5
D)54.5

Question 19

Does income increase when you get married? To investigate this,a college student has randomly selected people from his college town and collected income data for these people.They were categorized according to their marital status.The following results (in thousands of dollars)were obtained. The data are to be analyzed using the Wilcoxon rank sum test.The null hypothesis is that income has the same distribution for married and unmarried people.What is the appropriate alternative hypothesis?

A)The distribution of income for married people has values that are systematically larger than for unmarried people.
B)The distribution of income for unmarried people has values that are systematically larger than for married people.
C)The distribution of income for one of the two groups of people has values that are systematically larger than for the other group.
D)None of the above

Question 20

Does income increase when you get married? To investigate this,a college student has randomly selected people from his college town and collected income data for these people.They were categorized according to their marital status.The following results (in thousands of dollars)were obtained. The data are to be analyzed using the Wilcoxon rank sum test.Let W be the Wilcoxon rank sum test statistic equal to the sum of the ranks assigned to the married group.Using the Normal approximation with the continuity correction,what is the P-value for this test?

A)0.072
B)0.087
C)0.105
D)0.175

Question 21

A private university is trying to determine if there is pay equity among the male and female faculty.A simple random sample of six faculty members was selected from each gender group and the salary was recorded.The data (in thousands)are shown below. Rank all of the observations together.What is the list of ranks for the female group?

A)10,3,4,7,9,1
B)6,12,2,5,11,8
C)6,2,3,4,5,1
D)None of the above

Question 22

When using the Wilcoxon signed rank test and the absolute difference for a pair of observations is zero,it is best to _________________.

A)assign the absolute difference for the pair a value of 0.1
B)drop the pair from the study
C)assign the absolute difference for the pair any random value
D)None of the above

Question 23

The Wilcoxon signed rank test is for use with ________.

A)matched pairs studies
B)observations studies
C)randomized comparative experiments
D)None of the above

Question 24

In a study to investigate the effect of diet on reducing cholesterol levels,a random sample of five subjects known to have high cholesterol had their cholesterol measured at the beginning of the study and after 6 months on a special diet.The data are given in the table below. The data are to be analyzed using the Wilcoxon signed rank test.The five differences are to be assigned an appropriate rank.What rank should the difference of -7 be assigned?

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

Question 25

A private university is trying to determine if there is pay equity among the male and female faculty.A simple random sample of six faculty members was selected from each gender group and the salary was recorded.The data (in thousands)are shown below. What is the sum of the ranks for the female group?

A)44
B)34
C)78
D)None of the above

Question 26

"Cramming" is a technique often used by students to prepare for exams,in which they study for extended hours only a few days before the exams.Often students drink caffeinated beverages to help them stay awake while cramming for exams.Five students were randomly selected and asked to drink highly caffeinated beverages before their first midterm exam and then drink only water before their second midterm exam in the same subject.The difference of the scores (midterm 2 - midterm 1)is shown below for the five students. What is the value of,W⁺,the Wilcoxon signed rank test statistic? (Note: Use the positive difference. )

A)3
B)12
C)Cannot tell from the given information
D)None of the above

Question 27

"Cramming" is a technique often used by students to prepare for exams,in which they study for extended hours only a few days before the exams.Often students drink caffeinated beverages to help them stay awake while cramming for exams.Five students were randomly selected and asked to drink highly caffeinated beverages before their first midterm exam and then drink only water before their second midterm exam in the same subject.The difference of the scores (midterm 2 - midterm 1)is shown below for the five students. Using the continuity correction,what is the probability that needs to be calculated in order to obtain the P-value used to test the null hypothesis of no difference using the Wilcoxon signed rank test statistic?

A)P(W⁺  12)
B)P(W⁺  11.5)
C)P(W⁺  12.5)
D)None of the above

Question 28

"Cramming" is a technique often used by students to prepare for exams,in which they study for extended hours only a few days before the exams.Often students drink caffeinated beverages to help them stay awake while cramming for exams.Five students were randomly selected and asked to drink highly caffeinated beverages before their first midterm exam and then drink only water before their second midterm exam in the same subject.The difference of the scores (midterm 2 - midterm 1)is shown below for the five students. What is the standard deviation of,W⁺,the Wilcoxon signed rank test statistic?

A)3
B)12
C)Cannot be determined from the given information
D)None of the above

Question 29

A private university is trying to determine if there is pay equity among the male and female faculty.A simple random sample of six faculty members was selected from each gender group and the salary was recorded.The data (in thousands)are shown below. What is the standard deviation for the sum of the ranks for the male faculty?

A)2.5
B)3.6
C)10.2
D)None of the above

Question 30

A private university is trying to determine if there is pay equity among the male and female faculty.A simple random sample of six faculty members was selected from each gender group and the salary was recorded.The data (in thousands)are shown below. What is the sum of the ranks for the male group?

A)44
B)34
C)78
D)None of the above

Question 31

A private university is trying to determine if there is pay equity among the male and female faculty.A simple random sample of six faculty members was selected from each gender group and the salary was recorded.The data (in thousands)are shown below. Rank all the observations together.What is the list of ranks for the male group?

A)10,3,4,7,9,1
B)6,12,2,5,11,8
C)3,6,1,2,5,4
D)None of the above

Question 32

"Cramming" is a technique often used by students to prepare for exams,in which they study for extended hours only a few days before the exams.Often students drink caffeinated beverages to help them stay awake while cramming for exams.Five students were randomly selected and asked to drink highly caffeinated beverages before their first midterm exam and then drink only water before their second midterm exam in the same subject.The difference of the scores (midterm 2 - midterm 1)is shown below for the five students. Using the normal approximation with the continuity correction,what is the P-value used to test the null hypothesis of no difference against the alternative hypothesis that midterm 2 scores are systematically higher than midterm 1 scores using the Wilcoxon signed rank test statistic?

A).14
B).28
C).05
D)None of the above

Question 33

A private university is trying to determine if there is pay equity among the male and female faculty.A simple random sample of six faculty members was selected from each gender group and the salary was recorded.The data (in thousands)are shown below. What is the mean of the sum of the ranks for the male faculty?

A)18
B)36
C)39
D)None of the above

Question 34

"Cramming" is a technique often used by students to prepare for exams,in which they study for extended hours only a few days before the exams.Often students drink caffeinated beverages to help them stay awake while cramming for exams.Five students were randomly selected and asked to drink highly caffeinated beverages before their first midterm exam and then drink only water before their second midterm exam in the same subject.The difference of the scores (midterm 2 - midterm 1)is shown below for the five students. Using the normal approximation with the continuity correction,compute the P-value used to test the null hypothesis of no difference against the alternative hypothesis that midterm 2 scores are systematically higher than midterm 1 scores using the Wilcoxon signed rank test statistic.Using a significance level of .05,is there evidence against the null hypothesis of no systematic difference in the scores?

A)Yes
B)No

Question 35

In a study to investigate the effect of diet on reducing cholesterol levels,a random sample of five subjects known to have high cholesterol had their cholesterol measured at the beginning of the study and after 6 months on a special diet.The data are given in the table below. The data are to be analyzed using the Wilcoxon signed rank test.Under the null hypothesis that the responses have a continuous distribution that is not affected by the treatment,what is the expected value of the test statistic W⁺?

A)7.5
B)9.8
C)15
D)27.5

Question 36

In a study to investigate the effect of diet on reducing cholesterol levels,a random sample of five subjects known to have high cholesterol had their cholesterol measured at the beginning of the study and after 6 months on a special diet.The data are given in the table below. The data are to be analyzed using the Wilcoxon signed rank test.What is the observed value of W⁺?

A)7.5
B)13
C)21
D)34

Question 37

The Wilcoxon rank sum test will accurately test the hypotheses H₀: median₁ = median₂ vs H_a: median₁ > median₂ as long as what additional assumption is met?

A)Both populations have distributions of the same shape.
B)Both populations come from a Normal distribution.
C)One of the populations comes from a Normal distribution.
D)None of the above

Question 38

"Cramming" is a technique often used by students to prepare for exams,in which they study for extended hours only a few days before the exams.Often students drink caffeinated beverages to help them stay awake while cramming for exams.Five students were randomly selected and asked to drink highly caffeinated beverages before their first midterm exam and then drink only water before their second midterm exam in the same subject.The difference of the scores (midterm 2 - midterm 1)is shown below for the five students. What is the mean of the Wilcoxon signed rank test statistic,W⁺,under the null hypothesis that there is no difference?

A)3
B)12
C)15
D)None of the above

Question 39

A private university is trying to determine if there is pay equity among the male and female faculty.A simple random sample of six faculty members was selected from each gender group and the salary was recorded.The data (in thousands)are shown below. Based on the Wilcoxon rank sum test,is there evidence that the male faculty make more money than the female faculty?

A)Yes,because the sum of the ranks is higher than the mean of the male faculty
B)No,because the sum of the ranks is lower than the mean of the male faculty
C)Yes,because the sum of the ranks is lower than the mean of the male faculty
D)None of the reasons given are appropriate.

Question 40

When ranking the absolute values of the difference of observations from smallest to largest for use with the Wilcoxon signed rank test and there is a tie,it is best to ___________.

A)assign all tied values the average of the ranks they occupy
B)randomly choose an order for all tied observations
C)assign all tied values the highest rank order possible
D)None of the above

Question 41

Which of the following statements about the Kruskal-Wallis test are FALSE?

A)The test involves random samples of sizes
From I populations.
B)The I samples must be independent.
C)The I populations must have a common standard deviation,.
D)The test essentially applies the one-way ANOVA to the ranks of the observations rather than to the original observations themselves.
E)The test statistic H has,approximately,a chi-square distribution with I - 1 degrees of freedom.

Question 42

Laureysens,et al.(2004)studied the concentration of aluminum in wood from a number of clones of poplar growing in an area with heavy pollution.The same clone was sampled and tested once in August and again in November.The researchers believed that the concentration of aluminum would be shown to be increasing over time and hence higher in November than in August.The following table gives the aluminum concentrations for twelve of the clones. The data are to be analyzed using the Wilcoxon signed rank test.The null hypothesis they established was that the values of aluminum concentrations in the 2 months have the same distribution.Under the null hypothesis,what are the values of the mean and standard deviation,respectively,of the statistic W⁺?

A)39,162.5
B)39,12.75
C)65,12.75
D)65,162.5
E)Not within ± 2 of any of the above

Question 43

As part of a large,ongoing diet study,some subjects of the study are taking part in an intensive exercise program for four weeks.Several variables are measured on these subjects,both at the beginning and at the end of the four-week period.Some of these variables are weight,cholesterol,and triglyceride level.One objective of this particular study is to assess the effect of diet and intense exercise on increasing triglyceride levels.The data for a simple random sample of nine of these subjects are given in the table below. The data are to be analyzed using the Wilcoxon signed rank test.Under the null hypothesis that triglyceride levels have the same distribution at the beginning and at the end of the study,what is the expected value of the test statistic W⁺?

A)20.25
B)22.5
C)24.75
D)37

Question 44

Laureysens,et al.(2004)studied the concentration of aluminum in wood from a number of clones of poplar growing in an area with heavy pollution.The same clone was sampled and tested once in August and again in November.The researchers believed that the concentration of aluminum would be shown to be increasing over time and hence higher in November than in August.The following table gives the aluminum concentrations for twelve of the clones. The data are to be analyzed using the Wilcoxon signed rank test.The null hypothesis they established was that the values of aluminum concentrations in the 2 months have the same distribution.Using the Normal approximation,what is the value of the test statistic used in testing the null hypothesis?

A)2.00
B)1.93
C)3.06
D)-2.64
E)Not within ± 0.05 of any of the above

Question 45

As part of a large,ongoing diet study,some subjects of the study are taking part in an intensive exercise program for four weeks.Several variables are measured on these subjects,both at the beginning and at the end of the four-week period.Some of these variables are weight,cholesterol,and triglyceride level.One objective of this particular study is to assess the effect of diet and intense exercise on increasing triglyceride levels.The data for a simple random sample of nine of these subjects are given in the table below. The data are to be analyzed using the Wilcoxon signed rank test.The data were entered into SPSS,and the following output was obtained. Wilcoxon Signed Rank Test If the test statistic W⁺ were to be based on negative differences,what would be the value of z,the standardized value of W⁺?

A)-1.718
B)0.086
C)1.718
D)3.65

Question 46

As part of a large,ongoing diet study,some subjects of the study are taking part in an intensive exercise program for four weeks.Several variables are measured on these subjects,both at the beginning and at the end of the four-week period.Some of these variables are weight,cholesterol,and triglyceride level.One objective of this particular study is to assess the effect of diet and intense exercise on increasing triglyceride levels.The data for a simple random sample of nine of these subjects are given in the table below. The data are to be analyzed using the Wilcoxon signed rank test.The null hypothesis is that triglyceride levels have the same distribution at the beginning and at the end of the study.What is the appropriate alternative hypothesis?

A)Triglyceride levels are systematically higher at the beginning of the study.
B)Triglyceride levels are systematically higher at the end of the study.
C)Triglyceride levels at the beginning of the study are systematically different from triglyceride levels at the end of the study.
D)None of the above

Question 47

As part of a large,ongoing diet study,some subjects of the study are taking part in an intensive exercise program for four weeks.Several variables are measured on these subjects,both at the beginning and at the end of the four-week period.Some of these variables are weight,cholesterol,and triglyceride level.One objective of this particular study is to assess the effect of diet and intense exercise on increasing triglyceride levels.The data for a simple random sample of nine of these subjects are given in the table below. The data are to be analyzed using the Wilcoxon signed rank test.Under the null hypothesis that triglyceride levels have the same distribution at the beginning and at the end of the study,what is the standard deviation of the test statistic W⁺?

A)4.77
B)7.14
C)8.44
D)36.44

Question 48

As part of a large,ongoing diet study,some subjects of the study are taking part in an intensive exercise program for four weeks.Several variables are measured on these subjects,both at the beginning and at the end of the four-week period.Some of these variables are weight,cholesterol,and triglyceride level.One objective of this particular study is to assess the effect of diet and intense exercise on increasing triglyceride levels.The data for a simple random sample of nine of these subjects are given in the table below. The data are to be analyzed using the Wilcoxon signed rank test.Arrange the ten observations in order and assign ranks.What rank does the difference of 6 receive?

A)2
B)4
C)5
D)6

Question 49

At what age do babies learn to crawl? Does it take longer to learn in the winter when babies are often bundled in clothes that restrict their movement? Data were collected from parents who brought their babies into the University of Denver Infant Study Center to participate in one of a number of experiments between 1988 and 1991.Parents reported the birth month and the age at which their child was first able to creep or crawl a distance of 4 feet within 1 minute.The resulting data were grouped by month of birth: January,May,and September. The data are to be analyzed with the Kruskal-Wallis test.The null hypothesis is that the crawling ages have the same distribution in all groups.What is the alternative hypothesis?

A)Not all three mean crawling ages are equal.
B)The mean crawling age in September is higher than the other 2 months.
C)The crawling times in September are systematically higher than in the other 2 months.
D)None of the above.

Question 50

In a study to investigate the effect of diet on reducing cholesterol levels,a random sample of five subjects known to have high cholesterol had their cholesterol measured at the beginning of the study and after 6 months on a special diet.The data are given in the table below. The data are to be analyzed using the Wilcoxon signed rank test.What is the standardized value z of W⁺?

A)0.40
B)0.95
C)1.48
D)3.51

Question 51

At what age do babies learn to crawl? Does it take longer to learn in the winter when babies are often bundled in clothes that restrict their movement? Data were collected from parents who brought their babies into the University of Denver Infant Study Center to participate in one of a number of experiments between 1988 and 1991.Parents reported the birth month and the age at which their child was first able to creep or crawl a distance of 4 feet within 1 minute.The resulting data were grouped by month of birth: January,May,and September. The data are to be analyzed with the Kruskal-Wallis test.Under the null hypothesis,what is the approximate distribution of H?

A)F(2,6)
B)N(,)
C)(2)
D)(3)

Question 52

As part of a large,ongoing diet study,some subjects of the study are taking part in an intensive exercise program for four weeks.Several variables are measured on these subjects,both at the beginning and at the end of the four-week period.Some of these variables are weight,cholesterol,and triglyceride level.One objective of this particular study is to assess the effect of diet and intense exercise on increasing triglyceride levels.The data for a simple random sample of nine of these subjects are given in the table below. The data are to be analyzed using the Wilcoxon signed rank test.The data were entered into SPSS,and the following output was obtained. Wilcoxon Signed Rank Test The objective of this study is to assess if diet and intense exercise increase triglyceride levels.According to the SPSS output,what is the value of the appropriate P-value for this test?

A)0.043
B)0.086
C)0.172
D)None of the above

Question 53

Laureysens,et al.(2004)studied the concentration of aluminum in wood from a number of clones of poplar growing in an area with heavy pollution.The same clone was sampled and tested once in August and again in November.The researchers believed that the concentration of aluminum would be shown to be increasing over time and hence higher in November than in August.The following table gives the aluminum concentrations for twelve of the clones. The data are to be analyzed using the Wilcoxon signed rank test.The null hypothesis they established was that the values of aluminum concentrations in the 2 months have the same distribution.What is the value of the statistic W⁺ used for the test of hypotheses?

A)W⁺ = 78
B)W⁺ = 65
C)W⁺ = 5.3
D)W⁺ = 13
E)W⁺ = 63.6

Question 54

At what age do babies learn to crawl? Does it take longer to learn in the winter when babies are often bundled in clothes that restrict their movement? Data were collected from parents who brought their babies into the University of Denver Infant Study Center to participate in one of a number of experiments between 1988 and 1991.Parents reported the birth month and the age at which their child was first able to creep or crawl a distance of 4 feet within 1 minute.The resulting data were grouped by month of birth: January,May,and September. The data are to be analyzed with the Kruskal-Wallis test.Under the null hypothesis,compute the approximate distribution of H.At the 5% significance level,would we reject the null hypothesis?

A)Yes
B)No
C)This cannot be determined from the information given.

Question 55

At what age do babies learn to crawl? Does it take longer to learn in the winter when babies are often bundled in clothes that restrict their movement? Data were collected from parents who brought their babies into the University of Denver Infant Study Center to participate in one of a number of experiments between 1988 and 1991.Parents reported the birth month and the age at which their child was first able to creep or crawl a distance of 4 feet within 1 minute.The resulting data were grouped by month of birth: January,May,and September. The data are to be analyzed with the Kruskal-Wallis test.What is the value of the Kruskal-Wallis statistic H for these data?

A)H = 2.77
B)H = 3.10
C)H = 3.76
D)H = 5.99

Question 56

Laureysens,et al.(2004)studied the concentration of aluminum in wood from a number of clones of poplar growing in an area with heavy pollution.The same clone was sampled and tested once in August and again in November.The researchers believed that the concentration of aluminum would be shown to be increasing over time and hence higher in November than in August.The following table gives the aluminum concentrations for twelve of the clones. The data are to be analyzed using the Wilcoxon signed rank test.The null hypothesis they established was that the values of aluminum concentrations in the 2 months have the same distribution.What should the researchers establish as the appropriate alternative hypothesis?

A)

B)Values of aluminum concentrations are not the same in the 2 months.
C)For the differences (November - August),H_a:
> 0.
D)Values of aluminum concentrations are systematically larger in November than in August.
E)

Question 57

As part of a large,ongoing diet study,some subjects of the study are taking part in an intensive exercise program for four weeks.Several variables are measured on these subjects,both at the beginning and at the end of the four-week period.Some of these variables are weight,cholesterol,and triglyceride level.One objective of this particular study is to assess the effect of diet and intense exercise on increasing triglyceride levels.The data for a simple random sample of nine of these subjects are given in the table below. The data are to be analyzed using the Wilcoxon signed rank test.The data were entered into SPSS,and the following output was obtained. Wilcoxon Signed Rank Test If the test statistic W⁺ were to be based on positive differences,what would be the value of W⁺?

A)2.67
B)6.17
C)8
D)37