A researcher wants to determine the efficacy of a training program directed at improving concentration, focus, and memory on college students.She selects a random sample of 16 individuals and has them take an initial assessment test before the training program.Then the individuals complete the training program, and at the end they take a final test that's comparable to the initial test.The results are shown in the following table: \[\begin{array} { | c | c | c | } \hline \text { Individ. } & \text { Before } & \text { After } \\ \hline 1 & 79 & 81 \\ \hline 2 & 74 & 73 \\ \hline 3 & 81 & 82.5 \\ \hline 4 & 75 & 82.5 \\ \hline 5 & 72.5 & 85 \\ \hline 6 & 75 & 90 \\ \hline 7 & 67.5 & 83.5 \\ \hline 8 & 57.5 & 72.5 \\ \hline 9 & 62.5 & 87.5 \\ \hline 10 & 77.5 & 80 \\ \hline 11 & 61.5 & 92.5 \\ \hline 12 & 57.5 & 80 \\ \hline 13 & 61.5 & 71 \\ \hline 14 & 72.5 & 84 \\ \hline 15 & 64 & 78.5 \\ \hline 16 & 71 & 97.5 \\ \hline \end{array}\] The analyst uses a Wilcoxon matched-pairs signed rank test with a 0.05 significance level.The test statistic T- = ______.

A) 136 B) 142 C) 134 D) 135 E) 152 A) 136 B) 142 C) 134 D) 135 E) 152

A quality control supervisor wishes to determine whether the following measurements are random: \[\begin{array}{l} \begin{array} { r r r r r r r r } 68.2 & 65 & 66.5 & 65 & 67.5 & 68 & 66 & 64.5 \\ 65.3 & 64.2 & 67.6 & 66.5 & 66.8 & 68.9 & 67 & 65 \\ \hline\\ \end{array}\\ \begin{array} { r r r r r r r | } \hline 65 & 67 & 68 & 71 & 68.5 & 63.6 & 64.7 \\ 71.5 & 70.7 & 66 & 68.5 & 70.5 & 69.5 & 70.1 \\ \hline \end{array} \end{array}\] For this purpose, the supervisor uses a previous median 67.9 and compares each measurement to the median.She determines that the number of runs is ______.

A) 9 B) 10 C) 11 D) 12 E) 13 A) 9 B) 10 C) 11 D) 12 E) 13

Exam 17: Nonparametric Statistics

The attention span of kindergarteners are measured in minutes.A teacher wants to see if there are differences in the attention span of kindergarteners at different times of day.Using a sample of five such children, their attention spans are measured at five different times throughout the day.Using the data in the table below and an alpha of 0.05, what is the appropriate conclusion? 9 am 11am nown 1pm 3pm Child 1 12 5 10 7 8 Child 2 10 6 9 8 12 Child 3 7 10 6 8 13 Child 4 11 8 5 4 10 Child 5 12 4 11 5 8

(Multiple Choice)

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Question 41

Suppose a research uses the Mann-Whitney test to determine if there is a difference in the volume of text messages sent by a high school student living in a rural area versus an urban area during the month of December.Eight rural high school students and 9 urban high school students were included in the study.If, among all 17, the U statistic is 29, n₁=8 and n₂ = 9, the conclusion at α=0.05 would be __________

(Multiple Choice)

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Question 42

If the Spearman correlation between variable A and variable B was 0.24, then what could be said about the correlation between these two variables?

(Multiple Choice)

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Question 43

In the Wilcoxon test of the differences between two populations, the value z statistic was calculated to be 1.80.If the level of significance is 0.05, which of the following decisions is appropriate?

(Multiple Choice)

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Question 44

A researcher wants to determine the efficacy of a training program directed at improving concentration, focus, and memory on college students.She selects a random sample of 16 individuals and has them take an initial assessment test before the training program.Then the individuals complete the training program, and at the end they take a final test that's comparable to the initial test.The results are shown in the following table: Individ. Before After 1 79 81 2 74 73 3 81 82.5 4 75 82.5 5 72.5 85 6 75 90 7 67.5 83.5 8 57.5 72.5 9 62.5 87.5 10 77.5 80 11 61.5 92.5 12 57.5 80 13 61.5 71 14 72.5 84 15 64 78.5 16 71 97.5 The analyst uses a Wilcoxon matched-pairs signed rank test with a 0.05 significance level.The test statistic T_- = ______.

(Multiple Choice)

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Question 45

The HYPERLINK "http://www.statisticssolutions.com/mann-whitney-u-test" Mann-Whitney U test is used to test whether three or more independent HYPERLINK "http://www.experiment-resources.com/sample-group.html" samples of observations are drawn from the same or identical distributions.

(True/False)

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Question 46

A disadvantage of nonparametric statistics is that the probability statements obtained from most nonparametric tests are not exact probabilities.

(True/False)

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Question 47

A quality control supervisor wishes to determine whether the following measurements are random: 68.2 65 66.5 65 67.5 68 66 64.5 65.3 64.2 67.6 66.5 66.8 68.9 67 65 65 67 68 71 68.5 63.6 64.7 71.5 70.7 66 68.5 70.5 69.5 70.1 For this purpose, the supervisor uses a previous median 67.9 and compares each measurement to the median.She determines that the number of runs is ______.

(Multiple Choice)

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Question 48

A Mann-Whitney U test was performed to determine if there were differences in the average compute time for Dallas residents versus Atlanta residents.The travel time for 22 commuters in Dallas was compared to the travel time for 28 commuters in Atlanta.The U statistic was calculated to be 58.0 based on the sample sizes of 22 and 28.What is the z value for this test?

(Multiple Choice)

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Question 49

Charles Clayton monitors the daily performance of his investment portfolio by recording a "+" or a "-" sign to indicate whether the portfolio's value increased or decreased from the previous day.His record for the last eighteen business days is "- + + - - - + - - + + + - + + + + -".The number of runs in this sample is _________.

(Multiple Choice)

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Question 50

The degree of association of two variables cannot be estimated when only ordinal-level data are available.

(True/False)

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Question 51

The attention span of kindergarteners are measured in minutes.A teacher wants to see if there are differences in the attention span of kindergarteners at different times of day.Using a sample of five such children, their attention spans are measured at five different times throughout the day.Using the data in the table below and an alpha of 0.05, what is the observed $\chi$ ²? 9 am 11am nown 1pm 3pm Child 1 12 5 10 7 8 Child 2 10 6 9 8 12 Child 3 7 10 6 8 13 Child 4 11 8 5 4 10 Child 5 12 4 11 5 8

(Multiple Choice)

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Question 52

If the Spearman correlation between variable A and variable B was -0.24, then what could be said about the correlation between these two variables?

(Multiple Choice)

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Question 53

Suppose a research uses the Mann-Whitney test to determine if there is a difference in the volume of text messages sent by a high school student living in a rural area versus an urban area during the month of December.Eight rural high school students and 9 urban high school students were included in the study.If, among all 17, the sum of the ranks W₁ produced from the rural high school students is 72, the U₁ statistic is __________

(Multiple Choice)

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Question 54

The sampling distribution of R, the number of runs, in the one-sample runs test for randomness of the observations in a large sample is approximately normal, if H₀ is true.

(True/False)

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Question 55

A researcher wants to study the effects of physical exercise on depression.She randomly selects a group of 24 individuals who are equally depressed.None of these individuals currently exercises.She then randomly assigns them in one of three groups: group 1 stays without exercising (sedentary group), group 2 exercises once a week, and group 3 exercises two times a week.Individuals in groups 2 and 3 meet with a personal trainer so they carry out a very similar exercise program (kinds of exercises and intensity).After two months, the researcher has all individuals take a depression-assessment test.The score of the test goes from 0 = totally miserable to 100 = complete satisfaction. The scores are shown in the following table: Group 1 Group 2 Group 3 25 24 35 15 16 22 20 19 31 17 24 32 23 25 31 21 25 29 19 21 33 18 18 35 The researcher uses a Kruskal-Wallis test and a significance level $\alpha$ = 0.05.The sum of the ranks for group 3, T₃_, is ______.

(Multiple Choice)

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Question 56

Personnel specialist, Steve Satterfield, is assessing a new supervisor's ability to follow company standards for evaluating employees.Steve has the new supervisor rate five hypothetical employees on a scale of one to ten.He is interested in how the new supervisor's ratings correlate with company norms for these benchmark cases. Employee 1 2 3 4 5 New Supervisor 8 8 9 7 5 Company Norm 8 6 10 4 4 The Spearman rank correlation coefficient is ___________.

(Multiple Choice)

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Question 57

Four types of bicycle tires are ridden in six different cities to see if the tires lasted about the same number of miles.If there are differences, then that tire could promote its durability to potential customers.Using the data in the table below and an alpha of 0.05, what is the critical value of $\chi$ ²? Tire A Tire B Tire C Tire D City 1 105 157 112 119 City 2 142 124 132 144 City 3 133 121 138 130 City 4 98 136 110 119 City 5 114 141 95 128 City 6 117 138 129 140

(Multiple Choice)

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Question 58

Nonparametric statistics are sometimes called _______________.

(Multiple Choice)

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Question 59

In the one-sample runs test for randomness of the observations in a large sample the sampling distribution of R, the number of runs, is approximately binomial.

(True/False)

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Question 60

If the Spearman correlation between variable A and variable B was 0.24, then what could be said about the correlation between these two variables?

In the Wilcoxon test of the differences between two populations, the value z statistic was calculated to be 1.80.If the level of significance is 0.05, which of the following decisions is appropriate?

The HYPERLINK "http://www.statisticssolutions.com/mann-whitney-u-test" Mann-Whitney U test is used to test whether three or more independent HYPERLINK "http://www.experiment-resources.com/sample-group.html" samples of observations are drawn from the same or identical distributions.

A disadvantage of nonparametric statistics is that the probability statements obtained from most nonparametric tests are not exact probabilities.

The degree of association of two variables cannot be estimated when only ordinal-level data are available.

If the Spearman correlation between variable A and variable B was -0.24, then what could be said about the correlation between these two variables?

The sampling distribution of R, the number of runs, in the one-sample runs test for randomness of the observations in a large sample is approximately normal, if H₀ is true.

Nonparametric statistics are sometimes called _______________.

In the one-sample runs test for randomness of the observations in a large sample the sampling distribution of R, the number of runs, is approximately binomial.

Introduction to Statistics and Business Analytics

Visualizing Data With Charts and Graphs

Descriptive Statistics

Probability

Discrete Distributions

Continuous Distributions

Sampling and Sampling Distributions

Statistical Inference: Estimation for Single Populations

Statistical Inference: Hypothesis Testing for Single Populations

Statistical Inferences About Two Populations

Analysis of Variance and Design of Experiments

Simple Regression Analysis and Correlation

Multiple Regression Analysis

Building Multiple Regression Models

Time-Series Forecasting and Index Numbers

Analysis of Categorical Data

Statistical Quality Control

Decision Analysis

Filters

Exam 17: Nonparametric Statistics

If the Spearman correlation between variable A and variable B was 0.24, then what could be said about the correlation between these two variables?

In the Wilcoxon test of the differences between two populations, the value z statistic was calculated to be 1.80.If the level of significance is 0.05, which of the following decisions is appropriate?

The HYPERLINK "http://www.statisticssolutions.com/mann-whitney-u-test" Mann-Whitney U test is used to test whether three or more independent HYPERLINK "http://www.experiment-resources.com/sample-group.html" samples of observations are drawn from the same or identical distributions.

A disadvantage of nonparametric statistics is that the probability statements obtained from most nonparametric tests are not exact probabilities.

The degree of association of two variables cannot be estimated when only ordinal-level data are available.

If the Spearman correlation between variable A and variable B was -0.24, then what could be said about the correlation between these two variables?

The sampling distribution of R, the number of runs, in the one-sample runs test for randomness of the observations in a large sample is approximately normal, if H0 is true.

Nonparametric statistics are sometimes called _______________.

In the one-sample runs test for randomness of the observations in a large sample the sampling distribution of R, the number of runs, is approximately binomial.

Introduction to Statistics and Business Analytics

Visualizing Data With Charts and Graphs

Descriptive Statistics

Probability

Discrete Distributions

Continuous Distributions

Sampling and Sampling Distributions

Statistical Inference: Estimation for Single Populations

Statistical Inference: Hypothesis Testing for Single Populations

Statistical Inferences About Two Populations

Analysis of Variance and Design of Experiments

Simple Regression Analysis and Correlation

Multiple Regression Analysis

Building Multiple Regression Models

Time-Series Forecasting and Index Numbers

Analysis of Categorical Data

Statistical Quality Control

Decision Analysis

Filters

The sampling distribution of R, the number of runs, in the one-sample runs test for randomness of the observations in a large sample is approximately normal, if H₀ is true.