Question 1

Find the critical value. Assume that the test is two-tailed and that n denotes the number of pairs of data.
 n=30, $\alpha = 0.05$= 0.05

Accepted Answer

A)   0.362 
B)   -0.362 
C)   ±0.306 
D)  $\pm 0.362$ 
A)   0.362 
B)   -0.362 
C)   ±0.306 
D)  $\pm 0.362$ D

Question 2

Explain what an efficiency rating is. You may use an example to explain this concept. Do comparable parametric or nonparametric tests have higher efficiency ratings?

Accepted Answer

Higher efficiency ratings have the effect that "significant" results typically require smaller samples. For example if
test A has an efficiency rating of 0.93 as compared to test B, that means that test A requires 100 sample
observations as compared to 93 sample observations for test B. Parametric tests have higher efficiency ratings.

Question 3

Four different judges each rank the quality of 20 different singers. What method can be used for agreement among the four judges?

Accepted Answer

A)  Kruskal-Wallis Test 
B)  Wilcoxon rank-sum test 
C)  Runs Test 
D)  Rank correlation 
A)  Kruskal-Wallis Test 
B)  Wilcoxon rank-sum test 
C)  Runs Test 
D)  Rank correlation A

Question 4

Use the sign test to test the indicated claim. A researcher wishes to test whether a particular diet has an effect on blood pressure. The blood pressure of 24 randomly selected adults is measured. After one month on the diet, each person's blood pressure is again measured. For
18 people, the second blood pressure reading was lower than the first, and for 6 people, the
Second blood pressure reading was higher than the first. At the 0.01 significance level, test the
Claim that the diet has an effect on blood pressure. What would be the value of the test
Statistic, x?

Accepted Answer

A)  19 
B)  6 
C)  13 
D)  5 
A)  19 
B)  6 
C)  13 
D)  5

Question 5

Provide the appropriate response. Describe the Wilcoxon signed-ranks test. What types of hypotheses is it used to test? What assumptions are made for this test?

Accepted Answer

The Wilcoxon signed-ranks test is simila

Question 6

Give at least two examples of nonparametric tests and their comparable parametric tests

Accepted Answer

Answers will vary. Some possible example

Question 7

Use the rank correlation coefficient to test for a correlation between the two variables. Use the sample data below to find the rank correlation coefficient and test the claim of correlation
between math and verbal scores. Use a significance level of 0.05. $$\begin{array} { l l l l l l l l l l } 
\text { Mathematics } & 347 & 440 & 327 & 456 & 427 & 349 & 377 & 398 & 425 \
\hline \text { Verbal } & 285 & 378 & 243 & 371 & 340 & 271 & 294 & 322 & 385
\end{array}$$

Accepted Answer

r_z=0.867 . Critical values:

Question 8

If the critical values for a run test (found from table A-10)are 8 and 19 and the G value is 17, what should your conclusion about randomness be?

Accepted Answer

A)  Reject randomness. 
B)  Fail to reject randomness. 
C)  Support randomness. 
A)  Reject randomness. 
B)  Fail to reject randomness. 
C)  Support randomness.

Question 9

Use the rank correlation coefficient to test for a correlation between the two variables. Ten trucks were ranked according to their comfort levels and their prices.
$\begin{array} { c c c } 
\text { Make } & \text { Comfort } & \text { Price } \
\hline \text { A } & 1 & 6 \
\text { B } & 6 & 2 \
\text { C } & 2 & 3 \
\text { D } & 8 & 1 \
\text { E } & 4 & 4 \
\text { F } & 7 & 8 \
\text { G } & 9 & 10 \
\text { H } & 10 & 9 \
\text { I } & 3 & 5 \
\text { J } & 5 & 7
\end{array}$
Find the rank correlation coefficient and test the claim of correlation between comfort and price. Use a significance level of  0.05 .

Accepted Answer

@#LAT-DLM&  =0.382 . Critical values: @#LAT-DLM& F

Question 10

Describe the sign test. What types of hypotheses is it used to test? What is the underlying concept?

Accepted Answer

The sign test compares the signs (negati

Question 11

A rank correlation coefficient is to be calculated for a collection of paired data. lie between -10 and 10. Which of the following could affect the value of the rank correlation coefficient?
I: Multiplying every value of one variable by 3
II: Interchanging the two variables
III: Adding 2 to each value of one variable
IV: Replacing every value of one variable by its absolute value

Accepted Answer

A)  I and IV 
B)  III 
C)  I 
D)  IV 
A)  I and IV 
B)  III 
C)  I 
D)  IV

Question 12

The following scatterpolt shows the percentage of the vote a candidate received in the 2004 senatoral elections according to the voter's income level based on an exit poll of the voters conducted bu CNN. The income levels 1-8 correspond to the followng income classes: 1=under $15,00; 2=$15-30,000; 3=$30-50,000; 4=$50=75,000; 5=$75-100,000; 6=$100-150,000; 7=$150=200,000; 8=$200,000 or more.  
Use the election scatterplot to the find the critical values corresponding to a  0.01  significance level used to test the null hypothesis of  Ps=0 .

Accepted Answer

A)   -0.881  and  0.881 
B)   -0.881 
C)   -0.738  and  0.738 
D)   0.881 
A)   -0.881  and  0.881 
B)   -0.881 
C)   -0.738  and  0.738 
D)   0.881

Question 13

Use the sign test to test the indicated claim. The waiting times (in minutes)of 28 randomly selected customers in a bank are given below. Use a significance level of 0.05 to test the claim that the population median is equal to 5.3 minutes. $\begin{array} { r r r r r r r } 
8.2 & 8.0 & 10.5 & 3.8 & 6.4 & 5.3 & 7.8 \
2.9 & 6.0 & 7.7 & 6.1 & 5.9 & 1.2 & 10.4 \
7.3 & 6.9 & 5.8 & 5.1 & 6.2 & 3.1 & 5.8 \
11.7 & 4.5 & 6.5 & 9.8 & 7.4 & 2.3 & 7.8
\end{array}$

Accepted Answer

H₀ : The median is equal to 5.3 minute

Question 14

Find the ranks corresponding to the ages of five statistics professors when they were hired: 47, 51, 47, 47, 48

Accepted Answer

A)  1, 3, 1, 1, 2 
B)  2, 5, 2, 2, 4 
C)  3, 5, 3, 3, 4 
D)  2, 4, 2, 2, 3 
A)  1, 3, 1, 1, 2 
B)  2, 5, 2, 2, 4 
C)  3, 5, 3, 3, 4 
D)  2, 4, 2, 2, 3

Question 15

Use the Wilcoxon rank-sum approach to test the claim that the two independent sample student grade averages at two colleges come from populations with equal medians. The sample data is listed below. Use a  0.05  level of significance, and assume that the samples were randomly selected.
$\begin{array} { l l l l l l l l l l l l } 
\text { College A } & 3.2 & 4.0 & 2.4 & 2.6 & 2.0 & 1.8 & 1.3 & 0.0 & 0.5 & 1.4 & 2.9 \
\hline \text { College B } & 2.4 & 1.9 & 0.3 & 0.8 & 2.8 & 3.0 & 3.1 & 3.1 & 3.1 & 3.5 & 3.5
\end{array}$

Accepted Answer

@#LAT-DLM&
Test statistic:  z=-1.18 . Cr

Question 16

The following scatterpolt shows the percentage of the vote a candidate received in the 2004 senatoral elections according to the voter's income level based on an exit poll of the voters conducted bu CNN. The income levels 1-8 correspond to the followng income classes: 1=under $15,00; 2=$15-30,000; 3=$30-50,000; 4=$50=75,000; 5=$75-100,000; 6=$100-150,000; 7=$150=200,000; 8=$200,000 or more.
 
Use the election scatterplot to determine whether there is a correlation between percentage of vote and income level at the  0.01  significance level with a null hypothesis of  Pz=0 .

Accepted Answer

A)  The test statistic is between the critical values, so we fail to reject the null hypothesis. There is no evidence to support a claim of correlation between percentage of vote and income level. 
B)  The test statistic is not between the critical values, so we fail to reject the null hypothesis. There is no evidence to support a claim of correlation between percentage of vote and income level. 
C)  The test statistic is between the critical values, so we reject the null hypothesis. There is sufficient evidence to support a claim of correlation between percentage of vote and income level. 
D)  The test statistic is not between the critical values, so we reject the null hypothesis. There is sufficient evidence to support a claim of correlation between percentage of vote and income level. 
A)  The test statistic is between the critical values, so we fail to reject the null hypothesis. There is no evidence to support a claim of correlation between percentage of vote and income level. 
B)  The test statistic is not between the critical values, so we fail to reject the null hypothesis. There is no evidence to support a claim of correlation between percentage of vote and income level. 
C)  The test statistic is between the critical values, so we reject the null hypothesis. There is sufficient evidence to support a claim of correlation between percentage of vote and income level. 
D)  The test statistic is not between the critical values, so we reject the null hypothesis. There is sufficient evidence to support a claim of correlation between percentage of vote and income level.

Question 17

When applying the runs test for randomness above and below the median for 12 dollar/Euro exchange rate highs, the test statistic is G = 2. What does that value tell us about the data?

Accepted Answer

This tells us that there are only two ru

Question 18

If test A has an efficiency rating of 0.94 as compared to test B, explain what that efficiency rating means. Do comparable nonparametric or parametric tests have higher efficiency
ratings?

Accepted Answer

Higher efficiency ratings have the effec

Question 19

Which statement is false about the Wilcoxon signed-ranks test?

Accepted Answer

A)  It is used for testing a claim that a population of matched pairs has the property that the
Matched pairs have differences with a median equal to zero. 
B)  It is used for testing a claim that a single population of individual values has a median
Equal to some claimed value. 
C)  It is used for testing a claim that a single population of individual values has a mean
Equal to some claimed value. 
D)  It is a nonparametric test. 
A)  It is used for testing a claim that a population of matched pairs has the property that the
Matched pairs have differences with a median equal to zero. 
B)  It is used for testing a claim that a single population of individual values has a median
Equal to some claimed value. 
C)  It is used for testing a claim that a single population of individual values has a mean
Equal to some claimed value. 
D)  It is a nonparametric test.

Question 20

Describe the sign test. What types of hypotheses is it used to test? What is the underlying concept?

Accepted Answer

The sign test compares the signs (negati

Find the critical value. Assume that the test is two-tailed and that n denotes the number of pairs of data. n=30, $\alpha = 0.05$ = 0.05

Explain what an efficiency rating is. You may use an example to explain this concept. Do comparable parametric or nonparametric tests have higher efficiency ratings?

Four different judges each rank the quality of 20 different singers. What method can be used for agreement among the four judges?

Provide the appropriate response. Describe the Wilcoxon signed-ranks test. What types of hypotheses is it used to test? What assumptions are made for this test?

Give at least two examples of nonparametric tests and their comparable parametric tests

If the critical values for a run test (found from table A-10)are 8 and 19 and the G value is 17, what should your conclusion about randomness be?

Describe the sign test. What types of hypotheses is it used to test? What is the underlying concept?

Find the ranks corresponding to the ages of five statistics professors when they were hired: 47, 51, 47, 47, 48

When applying the runs test for randomness above and below the median for 12 dollar/Euro exchange rate highs, the test statistic is G = 2. What does that value tell us about the data?

If test A has an efficiency rating of 0.94 as compared to test B, explain what that efficiency rating means. Do comparable nonparametric or parametric tests have higher efficiency ratings?

Which statement is false about the Wilcoxon signed-ranks test?

Describe the sign test. What types of hypotheses is it used to test? What is the underlying concept?

Introduction to Statistics

Exploring Data With Tables and Graphs

Describing, Exploring, and Comparing Data

Probability

Discrete Probability Distributions

Normal Probability Distributions

Estimating Parameters and Determining Sample Sizes

Hypothesis Testing

Inferences From Two Samples

Correlation and Regression

Goodness-Of-Fit and Contingency Tables

Analysis of Variance

Statistical Process Control

Filters

Exam 13: Nonparametric Tests

Find the critical value. Assume that the test is two-tailed and that n denotes the number of pairs of data. n=30, α=0.05\alpha = 0.05α=0.05 = 0.05

Explain what an efficiency rating is. You may use an example to explain this concept. Do comparable parametric or nonparametric tests have higher efficiency ratings?

Four different judges each rank the quality of 20 different singers. What method can be used for agreement among the four judges?

Provide the appropriate response. Describe the Wilcoxon signed-ranks test. What types of hypotheses is it used to test? What assumptions are made for this test?

Give at least two examples of nonparametric tests and their comparable parametric tests

If the critical values for a run test (found from table A-10)are 8 and 19 and the G value is 17, what should your conclusion about randomness be?

Describe the sign test. What types of hypotheses is it used to test? What is the underlying concept?

Find the ranks corresponding to the ages of five statistics professors when they were hired: 47, 51, 47, 47, 48

When applying the runs test for randomness above and below the median for 12 dollar/Euro exchange rate highs, the test statistic is G = 2. What does that value tell us about the data?

If test A has an efficiency rating of 0.94 as compared to test B, explain what that efficiency rating means. Do comparable nonparametric or parametric tests have higher efficiency ratings?

Which statement is false about the Wilcoxon signed-ranks test?

Describe the sign test. What types of hypotheses is it used to test? What is the underlying concept?

Introduction to Statistics

Exploring Data With Tables and Graphs

Describing, Exploring, and Comparing Data

Probability

Discrete Probability Distributions

Normal Probability Distributions

Estimating Parameters and Determining Sample Sizes

Hypothesis Testing

Inferences From Two Samples

Correlation and Regression

Goodness-Of-Fit and Contingency Tables

Analysis of Variance

Statistical Process Control

Filters

Find the critical value. Assume that the test is two-tailed and that n denotes the number of pairs of data. n=30, $\alpha = 0.05$ = 0.05