Question 1

Which one of the following nonparametric methods requires that we carry out a paired difference experiment?

Accepted Answer

A) Wilcoxon signed ranks test 
B) Sign test 
C) Kruskal-Wallis test 
D) Wilcoxon rank sum test 
A) Wilcoxon signed ranks test 
B) Sign test 
C) Kruskal-Wallis test 
D) Wilcoxon rank sum test

Question 2

Refer to the MegaStat/Excel output for the Wilcoxon signed ranks test given in the table below.  
At a significance level of .01,which one of the following rejection point conditions is correct regarding the null hypothesis H0: D1 and D2 are identical probability distributions and the alternative hypothesis of Ha: D1 is shifted to the left of D2.

Accepted Answer

A) T- ≤ 2 
B) T+ ≤ 2 
C) T- ≤ 0 
D) T- ≤ 6 
E) The smaller of T+ or T- is less than 8. 
A) T- ≤ 2 
B) T+ ≤ 2 
C) T- ≤ 0 
D) T- ≤ 6 
E) The smaller of T+ or T- is less than 8.

Question 3

Nonparametric tests can be more powerful than the corresponding t or F tests if the population distribution is highly skewed or nonnormal.

Accepted Answer

A) True 
 B)False

Question 4

If the population from which we sample is highly skewed to the right or to the left,then the population _________ might be a better measure of central tendency than the population mean.

Accepted Answer

A) median 
B) variance 
C) mode 
D) average 
A) median 
B) variance 
C) mode 
D) average

Question 5

Wax-com Electronics Inc.claims that a certain circuit board has a median operating life of less than 20,000 hours.A random sample of 25 such circuit boards showed 8 circuit boards failing before 20,000 hours and 17 circuit boards failing after 20,000 hours.Assume the useful life of the circuit board is not normally distributed and state the null hypothesis.

Accepted Answer

A) H0: Md ≥ 20,000 
B) H0: Md ≤ 20,000 
C) H0: Md 0: Md ≠ 20,000 
A) H0: Md ≥ 20,000 
B) H0: Md ≤ 20,000 
C) H0: Md 0: Md ≠ 20,000

Question 6

The Wilcoxon rank sum test is used to compare the locations of two _____________ populations.

Accepted Answer

A) dependent 
B) normal 
C) independent 
D) similar 
A) dependent 
B) normal 
C) independent 
D) similar

Question 7

A professional organization is attempting to determine whether salaries of hospital CFOs differ by geographical region.Five hospital CFOs were randomly selected from each of the following four regions of the United States: East,Midwest,South,and West.Each CFO was then asked his or her annual salary.The salary distributions were highly skewed.The table below summarizes the results of the Kruskal-Wallis test obtained from MegaStat/Excel. $$\begin{array}{l}
\text { Kruskal-Wallis Test }\
\begin{array} { c c c } 
\hline \text { Median } & n & \begin{array} { c } 
\text { Avg. } \
\text { Rank }
\end{array} \
\hline 59.00 & 5 & 17.20 \text { Group 1 } \
55.30 & 5 & 10.40 \text { Group 2 } \
54.10 & 5 & 9.10 \text { Group } 3 \
53.20 & 5 & 5.30 \text { Group } 4 \
\hline 55.70 & 20 & \text { Total } \
\hline & & 10.565 \mathrm { H } \text { (corrected for ties) } \
&&3 \text { df. } \
& & .0143 \text { p-value }
\end{array}
\end{array}$$
At a significance level of .05,the rejection point condition for the hypothesis test is:

Accepted Answer

A) Reject H0 if ?2 > 9.3484. 
B) Reject H0 if ?2 > 30.1435. 
C) Reject H0 if ?2 > 7.81473. 
D) Reject H0 if ?2 > .341846. 
E) Reject H0 if ?2 > 32.8523. 
A) Reject H0 if ?2 > 9.3484. 
B) Reject H0 if ?2 > 30.1435. 
C) Reject H0 if ?2 > 7.81473. 
D) Reject H0 if ?2 > .341846. 
E) Reject H0 if ?2 > 32.8523.

Question 8

Five years ago,the average starting salary of a new college graduate with a major in marketing was $34,000.A random sample of 10 graduates from this year's graduating class of a local university yielded the following starting salaries in thousands of dollars: 38,36,25,37,35,24,38,45,39,36.The local university wants to determine if the starting salaries have increased in the last five years.Assume that the population of starting salaries in marketing is not normally distributed.Which one of the following tests is appropriate for this problem?

Accepted Answer

A) Wilcoxon signed ranks test 
B) Wilcoxon rank sum test 
C) Sign test 
D) Kruskal-Wallis test 
E) Mann-Whitney test 
A) Wilcoxon signed ranks test 
B) Wilcoxon rank sum test 
C) Sign test 
D) Kruskal-Wallis test 
E) Mann-Whitney test

Question 9

Refer to the MegaStat/Excel output for the Wilcoxon rank sum test given in the table below.  
At a significance level of .05,which one of the following rejection point conditions is correct regarding the null hypothesis H0: D1 and D2 are identical probability distributions and the alternative hypothesis of Ha: D1 is shifted to the left of D2.

Accepted Answer

A) We reject H0 and conclude that there is very strong evidence that the median value of the first sample significantly differs from the median value of the second sample. 
B) We reject H0 and conclude that there is very strong evidence that the median value of the first sample is significantly less than the median value of the second sample. 
C) We do not reject H0 and conclude there is not sufficient evidence that the median value of the first sample is significantly less than the median value of the second sample. 
D) We do not reject H0 and conclude there is not sufficient evidence to conclude that the median value of the first sample is not significantly different than the median value of the second sample. 
E) We failed to reject H0 and conclude there is very strong evidence that the median value of the first sample is significantly less than the median value of the second samplE. 
A) We reject H0 and conclude that there is very strong evidence that the median value of the first sample significantly differs from the median value of the second sample. 
B) We reject H0 and conclude that there is very strong evidence that the median value of the first sample is significantly less than the median value of the second sample. 
C) We do not reject H0 and conclude there is not sufficient evidence that the median value of the first sample is significantly less than the median value of the second sample. 
D) We do not reject H0 and conclude there is not sufficient evidence to conclude that the median value of the first sample is not significantly different than the median value of the second sample. 
E) We failed to reject H0 and conclude there is very strong evidence that the median value of the first sample is significantly less than the median value of the second samplE.

Question 10

Which one of the following nonparametric methods can be used with a single population?

Accepted Answer

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

Question 11

Refer to the MegaStat/Excel output for the Wilcoxon rank sum test given in the table below.  
At a significance level of .05,which one of the following statements is correct regarding the following null hypothesis?
H0: D1 and D2 are identical probability distributions.

Accepted Answer

A) We reject H0 and conclude there is very strong evidence that the median value of the first sample significantly differs from the median value of the second sample. 
B) We reject H0 and conclude there is very strong evidence that the median value of the first sample is significantly less than the median value of the second sample. 
C) We do not reject H0 and conclude there is not sufficient evidence that the median value of the first sample is significantly less than the median value of the second sample. 
D) We failed to reject H0 and conclude there is insufficient evidence to conclude that the median value of the first sample is not significantly different from the median value of the second sample. 
E) We failed to reject H0 and conclude there is very strong evidence that the median value of the first sample is significantly greater than the median value of the second samplE. 
A) We reject H0 and conclude there is very strong evidence that the median value of the first sample significantly differs from the median value of the second sample. 
B) We reject H0 and conclude there is very strong evidence that the median value of the first sample is significantly less than the median value of the second sample. 
C) We do not reject H0 and conclude there is not sufficient evidence that the median value of the first sample is significantly less than the median value of the second sample. 
D) We failed to reject H0 and conclude there is insufficient evidence to conclude that the median value of the first sample is not significantly different from the median value of the second sample. 
E) We failed to reject H0 and conclude there is very strong evidence that the median value of the first sample is significantly greater than the median value of the second samplE.

Question 12

In a manufacturing facility producing fasteners,a foreman suspects that the diameter of the bolts produced by his first-shift workers is greater than the diameter of the bolts produced by his second-shift workers.He takes a sample of 5 bolts from the first shift and a sample of 4 bolts from the second shift and measures the diameters in inches.Below are the results from 5 first shift and 4 second-shift observations.The bolt diameter measurements are not normally distributed. $$\begin{array} { c c } 
& { \text { Bolt Diameter (inches) } } \
\text { 1st shift } & \text { 2nd shift } \
2.01 & 1.80 \
2.25 & 1.95 \
1.98 & 2.30 \
2.05 & 2.00 \
2.03 &
\end{array}$$
At ? = .05,can we conclude that his suspicion is correct?

Accepted Answer

A) Reject the null hypothesis,the diameter is greater for 1st shift versus 2nd shift. 
B) Do not reject the null hypothesis,there is no evidence that the diameters differ by shift.
$$\begin{array} { c c } 
 { \text { Bolt Diameter (inches) } } \
\text { 1st shift } & \text { 2nd shift } \
2.01 & 1.80 \
2.25 & 1.95 \
1.98 & 2.30 \
2.05 & 2.00 \
2.03 &
\end{array}$$ 
A) Reject the null hypothesis,the diameter is greater for 1st shift versus 2nd shift. 
B) Do not reject the null hypothesis,there is no evidence that the diameters differ by shift.
$$\begin{array} { c c } 
 { \text { Bolt Diameter (inches) } } \
\text { 1st shift } & \text { 2nd shift } \
2.01 & 1.80 \
2.25 & 1.95 \
1.98 & 2.30 \
2.05 & 2.00 \
2.03 &
\end{array}$$

Question 13

The Wilcoxon rank sum test and the Kruskal-Wallis test both require that we take independent random samples.

Accepted Answer

A) True 
 B)False

Question 14

Assume that the following data set is not normally distributed.
(21,18,4,9,14,16,17,12,15,8,7,5)
If Ha: Md > 6,then the p value is:

Accepted Answer

A) .0161 
B) .0029 
C) .0537 
D) .0322 
E) .0192 
A) .0161 
B) .0029 
C) .0537 
D) .0322 
E) .0192

Question 15

A cholesterol test was given to 10 heart patients with high cholesterol levels.The same 10 heart patients are then given a new cholesterol-reducing drug for six months.Before the patients begin taking the drug,they are told to maintain their current diets and eating habits so that the effect of the drug can be more effectively determined.After taking the drug for six months,the same patients are given a cholesterol test again.The cholesterol levels before and after taking the drug are given below.The cholesterol level readings are not normally distributed.At ? = .05,test to determine if the drug is helpful in reducing cholesterol levels. $$\begin{array} { c c c } 
& { \text { Cholesterol level } } \
\text { Patient } & \text { Before } & \text { After } \
1 & 210 & 205 \
2 & 208 & 204 \
3 & 185 & 186 \
4 & 215 & 207 \
5 & 192 & 193 \
6 & 218 & 214 \
7 & 170 & 178 \
8 & 196 & 190 \
9 & 220 & 212 \
10 & 215 & 204
\end{array}$$
)

Accepted Answer

A) Reject the null hypothesis. 
B) Do not reject the null hypothesis.
Reject $\mathrm { H } _ { 0 }$ if $T _ { - } \leq T _ { 0510 }$
$$T _ { .05,10 } = 11$$
$$\begin{array} { c c c c c c c } 
& \text { Cholesterol level } & & & & \
\text { Patient } & \text { Before } & \text { After } & \left( d _ { i } \right) & \left| d _ { i } \right| & \text { Ranks } & \text { Neg.Ranks } \
1 & 210 & 205 & 5 & 5 & 5 & \
2 & 208 & 204 & 4 & 4 & 3.5 & \
3 & 185 & 186 & - 1 & 1 & 1.5 & 1.5 \
4 & 215 & 207 & 8 & 8 & 8 & \
5 & 192 & 193 & - 1 & 1 & 1.5 & 1.5 \
6 & 218 & 214 & 4 & 4 & 3.5 & \
7 & 170 & 178 & - 8 & 8 & 8 & 8 \
8 & 196 & 190 & 6 & 6 & 6 & \
9 & 220 & 212 & 8 & 8 & 8 & \
10 & 215 & 204 & 11 & 11 & 10 &
\end{array}$$ 
A) Reject the null hypothesis. 
B) Do not reject the null hypothesis.
Reject $\mathrm { H } _ { 0 }$ if $T _ { - } \leq T _ { 0510 }$
$$T _ { .05,10 } = 11$$
$$\begin{array} { c c c c c c c } 
& \text { Cholesterol level } & & & & \
\text { Patient } & \text { Before } & \text { After } & \left( d _ { i } \right) & \left| d _ { i } \right| & \text { Ranks } & \text { Neg.Ranks } \
1 & 210 & 205 & 5 & 5 & 5 & \
2 & 208 & 204 & 4 & 4 & 3.5 & \
3 & 185 & 186 & - 1 & 1 & 1.5 & 1.5 \
4 & 215 & 207 & 8 & 8 & 8 & \
5 & 192 & 193 & - 1 & 1 & 1.5 & 1.5 \
6 & 218 & 214 & 4 & 4 & 3.5 & \
7 & 170 & 178 & - 8 & 8 & 8 & 8 \
8 & 196 & 190 & 6 & 6 & 6 & \
9 & 220 & 212 & 8 & 8 & 8 & \
10 & 215 & 204 & 11 & 11 & 10 &
\end{array}$$

Question 16

Five years ago,the average starting salary of a new college graduate with a major in marketing was $34,000.A random sample of 10 graduates from this year's graduating class of a local university yielded the following starting salaries in thousands of dollars: 28,36,25,37,35,24,38,45,39,36.The local university wants to determine if the median starting salary for marketing graduates has increased in the last five years.
Assume that the population of starting salaries in marketing is not normally distributed.Using α = .05,can we conclude that the starting salaries increased in the last five years?

Accepted Answer

A) Reject the null hypothesis. 
B) Fail to reject the null hypothesis. 
A) Reject the null hypothesis. 
B) Fail to reject the null hypothesis.

Question 17

Two coffee-vending machines are studied to determine whether they distribute the same amounts.Samples are taken and the number of ounces is recorded for each machine. $$\begin{array} { c c } 
\text { Machine A } & \text { Machine B } \
\hline 6.10 & 5.99 \
5.95 & 6.01 \
5.98 & 5.98 \
6.01 & 5.96 \
6.00 & 6.08 \
5.95 & 5.89 \
6.02 & 6.01 \
6.04 & 6.00 \
5.99 & 5.97 \
6.06 & 6.00
\end{array}$$
On average,can we conclude that the machines distribute the same amount? Test at ? = .05.

Accepted Answer

A) Reject the null hypothesis. 
B) Do not reject the null hypothesis.
$\begin{array}{ccc}
 \text {  }&\text { Machine A } & & \text { Machine B } \
 \text {  }& 20 & & 9.5 \
 \text {  }&3.5 & & 13.5 \
 \text {  }&7.5 & & 7.5 \
 \text {  }&13.5 & & 5 \
 \text {  }&11.5 & & 19 \
 \text {  }&3.5 & & 1 \
 \text {  }&15 & & 18 \
 \text {  }&16 & & 11.5 \
 \text {  }&9.5 & & 6 \
 \text {  }&17 & & 2 \
 \text { TOTAL }&117 &&  93
\end{array}$ 
A) Reject the null hypothesis. 
B) Do not reject the null hypothesis.
$\begin{array}{ccc}
 \text {  }&\text { Machine A } & & \text { Machine B } \
 \text {  }& 20 & & 9.5 \
 \text {  }&3.5 & & 13.5 \
 \text {  }&7.5 & & 7.5 \
 \text {  }&13.5 & & 5 \
 \text {  }&11.5 & & 19 \
 \text {  }&3.5 & & 1 \
 \text {  }&15 & & 18 \
 \text {  }&16 & & 11.5 \
 \text {  }&9.5 & & 6 \
 \text {  }&17 & & 2 \
 \text { TOTAL }&117 &&  93
\end{array}$

Question 18

Parametric tests,such as F and t tests,are more powerful than their nonparametric counterparts if the assumptions needed to perform the parametric test are not violated.

Accepted Answer

A) True 
 B)False

Question 19

Which one of the following nonparametric methods can be used to compare more than two independent populations in a single test?

Accepted Answer

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

Which one of the following nonparametric methods requires that we carry out a paired difference experiment?

Nonparametric tests can be more powerful than the corresponding t or F tests if the population distribution is highly skewed or nonnormal.

If the population from which we sample is highly skewed to the right or to the left,then the population _________ might be a better measure of central tendency than the population mean.

The Wilcoxon rank sum test is used to compare the locations of two _____________ populations.

Which one of the following nonparametric methods can be used with a single population?

Refer to the MegaStat/Excel output for the Wilcoxon rank sum test given in the table below. At a significance level of .05,which one of the following statements is correct regarding the following null hypothesis? H₀: D₁ and D₂ are identical probability distributions.

The Wilcoxon rank sum test and the Kruskal-Wallis test both require that we take independent random samples.

Assume that the following data set is not normally distributed. (21,18,4,9,14,16,17,12,15,8,7,5) If H_a: M_d > 6,then the p value is:

Parametric tests,such as F and t tests,are more powerful than their nonparametric counterparts if the assumptions needed to perform the parametric test are not violated.

Which one of the following nonparametric methods can be used to compare more than two independent populations in a single test?

Statistical Inferences for Population Variances

Experimental Design and Analysis of Variance

Chi-Square Tests

Simple Linear Regression Analysis

Multiple Regression and Model Building

Time Series Forecasting and Index Numbers

Process Improvement Using Control Charts

Decision Theory

Filters

Exam 18: Nonparametric Methods

Which one of the following nonparametric methods requires that we carry out a paired difference experiment?

Nonparametric tests can be more powerful than the corresponding t or F tests if the population distribution is highly skewed or nonnormal.

If the population from which we sample is highly skewed to the right or to the left,then the population _________ might be a better measure of central tendency than the population mean.

The Wilcoxon rank sum test is used to compare the locations of two _____________ populations.

Which one of the following nonparametric methods can be used with a single population?

Refer to the MegaStat/Excel output for the Wilcoxon rank sum test given in the table below. At a significance level of .05,which one of the following statements is correct regarding the following null hypothesis? H0: D1 and D2 are identical probability distributions.

The Wilcoxon rank sum test and the Kruskal-Wallis test both require that we take independent random samples.

Assume that the following data set is not normally distributed. (21,18,4,9,14,16,17,12,15,8,7,5) If Ha: Md > 6,then the p value is:

Parametric tests,such as F and t tests,are more powerful than their nonparametric counterparts if the assumptions needed to perform the parametric test are not violated.

Which one of the following nonparametric methods can be used to compare more than two independent populations in a single test?

Statistical Inferences for Population Variances

Experimental Design and Analysis of Variance

Chi-Square Tests

Simple Linear Regression Analysis

Multiple Regression and Model Building

Time Series Forecasting and Index Numbers

Process Improvement Using Control Charts

Decision Theory

Filters

Refer to the MegaStat/Excel output for the Wilcoxon rank sum test given in the table below. At a significance level of .05,which one of the following statements is correct regarding the following null hypothesis? H₀: D₁ and D₂ are identical probability distributions.

Assume that the following data set is not normally distributed. (21,18,4,9,14,16,17,12,15,8,7,5) If H_a: M_d > 6,then the p value is: