Deck 18: Nonparametric Methods

Question 1

The sign test is a nonparametric test for a population mean that is valid for any sample size and population shape.

Answer 1

False

Question 2

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

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

Answer 2

C

Question 3

An assumption of the Wilcoxon rank sum test is that the variances of the two populations are equal.

Answer 3

True

Question 4

If you have data that consist of matched pairs collected from two dependent populations,then it may be appropriate to use the Wilcoxon signed ranks test.

Question 5

In testing the significance of a population correlation coefficient using the Spearman's rank correlation coefficient,it is assumed that all possible combinations of values of variable X and variable Y have a bivariate normal probability distribution.

Question 6

The Wilcoxon rank sum test requires that two independent samples being compared must have equal sample sizes.

Question 7

The Kruskal-Wallis test requires that all p samples being compared must have equal sample sizes.

Question 8

A sign test is a test of hypothesis about the population mean.

Question 9

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

Question 10

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.

Question 11

A parametric test is always more powerful than its nonparametric counterpart.

Question 12

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

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

Question 13

The sign test is a test about a population median that is valid for any sample size and population shape.

Question 14

The Spearman's rank correlation test can be used to study the relationship between two ordinal variables.

Question 15

Which of the following statements about nonparametric methods is correct?

A)Nonparametric methods are only used in cases where parametric tests such as t or F do not exist.
B)Nonparametric tests should always be used when one is available because they are easier to apply then their parametric counterparts.
C)Nonparametric tests are useful alternatives to parametric tests such as t or F when certain assumptions required by parametric tests are violated.
D)Nonparametric tests are only used if the data come from independent samples.

Question 16

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

Question 17

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

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

Question 18

The Wilcoxon rank sum test is a nonparametric test used to compare the central tendencies of two populations when a paired difference experiment has been conducted.

Question 19

The Wilcoxon signed ranks test is also called the Mann-Whitney test.

Question 20

The Wilcoxon signed ranks test is a nonparametric test.

Question 21

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:

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

Question 22

An e-business/e-commerce information technology consulting company wants to compare the effectiveness of three programming languages that its programmers use.Currently each programming language is used by approximately 1/3 of the programmers employed by the company.The director of the programming division randomly selected 5 programmers from the users of each of the three programming languages and assigned the same simple programming task to each programmer.It is known that all three populations have highly skewed distributions with extreme outliers.Which one of the following nonparametric tests is appropriate for this problem?

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

Question 23

Which one of the following nonparametric methods can be used to determine the strength of the relationship between two variables?

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

Question 24

In a manufacturing facility producing fasteners,a foreman suspects that the diameter of the bolts produced by his second-shift workers is greater than the diameter of the bolts produced by his first-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.The population of bolt diameter measurements is not normally distributed.Which one of the following nonparametric tests is appropriate for this problem?

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

Question 25

Two NFL scouts are in the process of recruiting 7 college senior football players (receivers).After a careful review and evaluation,both scouts ranked the seven receivers in terms of their professional career prospects.If we want to determine whether the two scouts have similar opinions about the professional football career prospects of the seven players,which one of the following nonparametric tests would we choose?

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

Question 26

The EPA has stipulated that the Pollution Standard Index (PSI)for clean air standards is to average no more than 100.A random sample of 9 days for the city of Acorn showed PSI readings of 144,85,90,120,150,105,93,130,and 115.Assume the population of PSI readings is highly nonnormal.The EPA wants to determine if there is significant evidence to conclude that Acorn's air is dirtier than the stipulated clean air standards.Which one of the following tests is appropriate for this problem?

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

Question 27

Parametric methods are ____________ more powerful than their nonparametric counterparts.

A)Always
B)Sometimes
C)Never

Question 28

The __________________ is a general test to detect whether the probability distribution of one population is shifted to the right or to the left of the probability distribution of another population.

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

Question 29

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.

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 30

The Kruskal-Wallis test is the nonparametric counterpart of the:

A)Large sample test about a single population mean.
B)Two independent samples t test.
C)One way ANOVA F test.
D)Paired difference t test.
E)F test for equality of population variances.

Question 31

Which one of the following nonparametric methods can be considered as an extension of the Wilcoxon rank sum test?

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

Question 32

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?

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

Question 33

The Wilcoxon signed ranks test is the nonparametric counterpart of the:

A)Large sample test about a single population mean.
B)Two independent samples t test.
C)One way ANOVA F test.
D)Paired difference t test.
E)F test for equality of population variances.

Question 34

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 pharmaceutical company manufacturing the medicine wants to know if the drug is effective in reducing the cholesterol levels of the patients.The cholesterol levels before and after taking the drug are recorded for each patient.The population of cholesterol levels is not normally distributed.Which one of the following nonparametric tests is appropriate for this problem?

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

Question 35

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 < 16,then the p value is:

A).1208
B).1937
C).0537
D).3874
E).1458

Question 36

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 following null hypothesis?
H₀: D₁ and D₂ are identical probability distributions.

A)Reject H₀ if T ≥ 79 or T ≤ 131
B)Reject H₀ if T ≥ 131 or T ≤ 83
C)Reject H₀ if T ≥ 131 or T ≤ 79
D)Reject H₀ if T ≤ 83 or T ≥ 127
E)Reject H₀ if T ≤ 79 or T ≥ 127

Question 37

The signed ranks test is the nonparametric counterpart of the:

A)Small sample t test about a single population mean.
B)Two independent samples t test.
C)One way ANOVA F test.
D)Paired difference t test.
E)F test for equality of population variances.

Question 38

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 ≠ 7,then the p value is:

A).0161
B).0029
C).1458
D).0729
E).0537

Question 39

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 value of S is:

A)0.
B)1.
C)2.
D)3.
E)4.

Question 40

The Wilcoxon rank sum test is the nonparametric counterpart of the:

A)Large sample test about a single population mean.
B)Two independent samples t test.
C)F test.
D)Paired difference t test.
E)F test for equality of population variances.

Question 41

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.

A)H₀: M_d ≥ 20,000
B)H₀: M_d ≤ 20,000
C)H₀: M_d < 20,000
D)H₀: M_d ≠ 20,000

Question 42

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.

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

Question 43

In order to perform the ________________ test,all of the observations in two samples are combined into a single set and all of the values in the single set are ranked from smallest to largest.

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

Question 44

A ___________ test is a statistical test that can be used without assuming that the sampled population(s)has/have a particular type of probability distribution.

A)Wilcoxon rank sum
B)Nonparametric
C)Linear regression
D)Correlation

Question 45

The __________________ test is a nonparametric counterpart of a one-way ANOVA F test.

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

Question 46

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 H_a: D₁ is shifted to the left of D₂.

A)We reject H₀ and conclude there is not sufficient evidence that the probability distribution of population 1 is shifted to the left of the probability distribution of population 2.
B)We cannot reject H₀ and conclude there is not sufficient evidence that the probability distribution of population 1 is shifted to the left of the probability distribution of population 2.
C)We reject H₀ and conclude there is very strong evidence that the probability distribution of population 1 is shifted to the left of the probability distribution of population 2.
D)We failed to reject H₀ and conclude there is very strong evidence that the probability distribution of population 1 is shifted to the left or to the right of the probability distribution of population 2.
E)We failed to reject H₀ and conclude there is very strong evidence that the probability distribution of population 1 is identical to the probability distribution of population 2.

Question 47

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,which one of the following statements is correct regarding the following null hypothesis?
H₀: The four populations under consideration have identical locations.

A)We reject H₀ and conclude that there is very strong evidence that the median hospital CFO salaries differ among all four regions in the United States.
B)We failed to reject H₀ and conclude that there is not sufficient evidence that the median hospital CFO salaries differ among any of the four regions of the United States.
C)We do not reject H₀ and conclude that there is only adequate evidence that the median hospital CFO salaries differ between at least two of the four regions in the United States.
D)We reject H₀ and conclude that there is strong evidence that the median hospital CFO salaries differ between at least two of the four regions in the United States.
E)We do not reject H₀ and conclude that all 4 populations under consideration are identical in their locations.

Question 48

The Kruskal-Wallis H statistic can be approximated by the _____________ distribution.

A)Normal
B)Chi-square
C)z
D)t

Question 49

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 H_a: D₁ is shifted to the left of D₂.

A)Reject H₀ if T ≥ 83
B)Reject H₀ if T ≤ 127
C)Reject H₀ if T ≥ 131
D)Reject H₀ if T ≤ 83
E)Reject H₀ if T ≤ 79

Question 50

In a local ice skating contest,there were 2 judges and 15 contestants.Each judge was asked to rate each contestant on a 7-point scale.The most successful candidates received a rating value of 7,while the least successful candidates received a rating value of 1.It appears that the bivariate normal probability distribution assumption was severely violated.The City Council wants to know whether the judges have similar opinions in rating ice skating competitors.At a significance level of .01,the rejection point condition for the hypothesis test is:

A)Reject H₀ if r_s > .457.
B)Reject H₀ if r_s > .623.
C)Reject H₀ if r_s > .441.
D)Reject H₀ if r_s > .646.
E)Reject H₀ if r_s > .689.

Question 51

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

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

Question 52

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.At ? = .05,can it be concluded that the sample contradicts the company's claim? Assume the useful life of the circuit board is not normally distributed.

A)Reject the null hypothesis.
B)Do not reject the null hypothesis.
$$Z = \frac { 8.5 - 25 ( .5 ) } { \sqrt { ( .5 ) ( 1 - .5 ) ( 25 } } = \frac { - 4 } { 2.5 } = - 1.6$$

Question 53

In a Wilcoxon rank sum test,when two or more observations are equal,we assign to each tied observation a rank equal to the _________ of the consecutive ranks.

A)average
B)median
C)sum
D)difference

Question 54

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:

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 55

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 H_a: D₁ is shifted to the left of D₂.

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

Question 56

The ______________ test is a nonparametric method that requires data consisting of matched pairs.

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

Question 57

The __________________ test is a nonparametric counterpart of a small-sample t test for comparing two independent population locations.

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

Question 58

In order to perform the ________________ test,all of the observations in p samples are combined into a single set and all of the values in the single set are ranked from smallest to largest.After ranking,the sum of the ranks for each of the p samples is calculated.

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

Question 59

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 H_a: D₁ is shifted to the left of D₂.

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 60

When a large sample is taken,the _______________ approximation to the binomial distribution can be used to implement the sign test.

A)chi-square
B)normal
C)correlation coefficient
D)rank sum

Question 61

We have the following sample data: .980,1.01,.970,.990,1.00,1.00,.980,.970,.980,and .999.Run a sign test on H₀: M_d = 1.00 with a 2-sided alternative at α = .05.What do you conclude?

A)Reject the null hypothesis,I value = .0352
B)Do not reject the null hypothesis,p value = .004
C)Reject the null hypothesis,p value = .004
D)Do not reject the null hypothesis,p value = .0352

Question 62

Three years ago,a major hotel chain purchased a large number of heating and air-conditioning units from three major manufacturers,A,B,and

A)Reject the null hypothesis.
B)Fail to reject the null hypothesis.
$\begin{array}{lrcrcr}\text { Brand A } & \left(R_{A}\right) & \text { Brand B } & \left(R_{B}\right) & \text { Brand C } & \left(R_{C}\right) \\\$ 80 & (2) & \$ 100 & (4) & \$ 140 & (6) \\\$ 250 & (10.5) & \$ 170 & (8) & \$ 280 & (12) \\\$ 150 & (7) & \$ 430 & (19) & \$ 100 & (4) \\\$ 70 & (1) & \$ 290 & (13) & \$ 100 & (4) \\\$ 220 & (9) & \$ 370 & (17) & \$ 340 & (15) \\\$ 300 & \underline{(14)} & \$ 420 & (18) & \$ 250 & (10.5) \\& 43.5 & \$ 350 & \underline{(16)}& &51.5\\&&&95&&\end{array}$

$$\begin{array} { l } \chi _ { .05,2 } ^ { 2 } = 5.99 \\H = \frac { 12 } { ( 19 ) ( 20 ) } \left[ \frac { ( 43.5 ) ^ { 2 } } { 6 } + \frac { ( 95 ) ^ { 2 } } { 7 } + \frac { ( 51.5 ) ^ { 2 } } { 6 } \right] - 3 ( 19 + 1 ) \\H = 4.633\end{array}$$
C)The accounting department of the hotel chain kept records on their repair and replacement costs over the last 3 years.The manager of the purchasing department randomly selected 6 brand A,7 brand B,and 6 brand C heating and air-conditioning unit records.The repair and replacement costs in dollars are summarized in the following table.At ? = .05,can we conclude that there is a significant difference in repair costs among the three brands?
$$\begin{array} { l c c } \text { Brand A } & \text { Brand B } & \text { Brand C } \\\$ 80 & \$ 100 & \$ 140 \\\$ 250 & \$ 170 & \$ 280 \\\$ 150 & \$ 430 & \$ 100 \\\$ 70 & \$ 290 & \$ 100 \\\$ 220 & \$ 370 & \$ 340 \\\$ 300 & \$ 420 & \$ 250\\&\$350\end{array}$$

Question 63

In an effort to improve productivity in its factory,a firm recently instituted a training program for its workers.One of the work crews consisted of 14 workers.Seven workers from this crew were selected at random to attend the training course.All seven workers selected successfully completed the training course.The remaining seven workers served as a control group and did not attend the training course.Three months after the training course,a foreman who did not know which employees attended the training course was asked to rank all 14 employees in terms of their productivity.A rank of 14 indicates the most productive employee in the crew,while a rank of 1 indicates the least productive worker. $$\begin{array} { c c } \text { Trained Ranks } & \text { Untrained Ranks } \\7 & 6 \\12 & 2 \\14 & 9 \\4 & 3 \\8 & 1 \\13 & 5 \\10 & 11\end{array}$$
At ? = .05,can it be concluded that training was beneficial in improving productivity?

A)Reject the null hypothesis;training is beneficial.
B)Do not reject the null hypothesis;we cannot determine if the training makes a difference.
$H _ { 0 } : D _ { \text {Trained } }$ and $D _ { \text {Untrained } }$ are identical probability distributions. or
$H _ { 0 } : \mu _ { D _ { \text {Trained} } } \leq \mu _ { D _ { \text {Untrained } } }$
$H _ { A } : D _ { \text {Trained } }$ is shifted to the right of $D _ { \text {Untrained } }$ or
$H_{A}: \mu_{D_{Trained }}>\mu_{D_{Untrained}}$

$$\begin{array} { l } T _ { \text {Trained } } = 68 \quad T _ { \text {Untrained } } = 37 \\\text { Reject } \mathrm { H } _ { 0 } \text { if } \mathrm { T } \geq \mathrm { T } _ { \mathrm { U } } \\T _ { U } = T _ { .05,7,7 } = 66\end{array}$$

Question 64

In an effort to improve productivity in its factory,a firm recently instituted a training program for its workers.One of the work crews consisted of 14 workers.Seven workers from this crew were selected at random to attend the training course.All seven workers selected successfully completed the training course.The remaining seven workers served as a control group and did not attend the training course.Three months after the training course,a foreman who did not know which employees attended the training course was asked to rank all 14 employees in terms of their productivity.A rank of 14 indicates the most productive employee in the crew,while a rank of 1 indicates the least productive worker. $$\begin{array} { c c } \text { Trained Ranks } & \text { Untrained Ranks } \\7 & 6 \\12 & 2 \\14 & 9 \\4 & 3 \\8 & 1 \\13 & 5 \\10 & 11\end{array}$$
State the null hypothesis for this problem.

A)H₀: D_T ? D_U
B)H₀: D_T ? D_U
C)H₀: D_T ? D_U
D)H₀: D_T > D_U

Question 65

The EPA has stipulated that the Pollution Standard Index (PSI)for clean air standards is to average no more than 100.A random sample of 9 days for the city of Acorn showed PSI readings of 144,85,90,120,150,105,93,130,and 115.Assume the population of PSI readings is highly nonnormal.The EPA wants to determine if there is significant evidence to conclude that Acorn's air is dirtier than the stipulated clean air standards.The test is conducted at α = .05 and the p value is found to be .254.Based on this result,provide a one-sentence managerial conclusion.

A)Acorn's air is dirtier than the EPA stipulated clean air standards.
B)We cannot conclude that Acorn's air is dirtier than the EPA stipulated clean air standards.
C)Acorn's air is better than the EPA stipulated clean air standards.
D)Acorn's air meets the EPA stipulated clean air standards.

Question 66

A random sample of 11 third-year medical school students took a comprehensive written exam as well as a comprehensive oral exam.The scores on both exams are given below.It is established that both test scores have highly nonnormal distributions. $$\begin{array} { c c c } \text { Student } & \text { Written exam score } & \text { Oral exam score } \\1 & 60 & 55 \\2 & 72 & 78 \\3 & 33 & 60 \\4 & 89 & 87 \\5 & 61 & 79 \\6 & 65 & 82 \\7 & 25 & 41 \\8 & 80 & 58 \\9 & 92 & 95 \\10 & 48 & 64 \\11 & 65 & 70\end{array}$$
At ? = .05,can we conclude that the oral exam scores are higher than the written exam scores?

A)Reject the null hypothesis.
B)Do not reject the null hypothesis.
$$\begin{array} { c c c c c c } \text { Student } & \text { Written exam score } & \text { Oral exam score } & d _ { i } & \left| d _ { i } \right| & \text { Rank of } \left| d _ { i } \right| \\1 & 60 & 55 & 5 & 5 & 3.5 \\2 & 72 & 78 & - 6 & 6 & 5 \\3 & 33 & 60 & - 27 & 27 & 11 \\4 & 89 & 87 & 2 & 2 & 1 \\5 & 61 & 79 & - 18 & 18 & 9 \\6 & 65 & 82 & - 17 & 17 & 8 \\7 & 25 & 41 & - 16 & 16 & 6.5 \\8 & 80 & 58 & 22 & 22 & 10 \\9 & 92 & 95 & - 3 & 3 & 2 \\10 & 48 & 64 & - 16 & 16 & 6.5 \\11 & 65 & 70 & - 5 & 5 & 3.5\end{array}$$

Question 67

A random sample of 11 third-year medical school students took a comprehensive written exam as well as a comprehensive oral exam.The scores on both exams are given below.It is established that both test scores have highly nonnormal distributions. $$\begin{array} { c c c } \text { Student } & \text { Written exam score } & \text { Oral exam score } \\1 & 60 & 55 \\2 & 72 & 78 \\3 & 33 & 60 \\4 & 89 & 87 \\5 & 61 & 79 \\6 & 65 & 82 \\7 & 25 & 41 \\8 & 80 & 58 \\9 & 92 & 95 \\10 & 48 & 64 \\11 & 65 & 70\end{array}$$
The medical examination board wants to know if the oral exam scores are higher than the written exam scores.State the appropriate null hypothesis for this problem.

A)H₀: The probability distribution of written exam scores is identical to the probability distribution of oral exam scores.
B)H₀: The probability distribution of written exam scores is shifted to the left of the probability distribution of oral exam scores.
C)H₀: The probability distribution of written exam scores is shifted to the right of the probability distribution of oral exam scores.
D)H₀: The probability distribution of written exam scores is shifted to the left or right of the probability distribution of oral exam scores.

Question 68

The EPA has stipulated that the Pollution Standard Index (PSI)for clean air standards is to average no more than 100.A random sample of 9 days for the city of Acorn showed PSI readings of 144,85,90,120,150,105,93,130,and 115.The EPA wants to test to determine if Acorn's air is dirtier than the stipulated clean air standards.Assume the population of PSI readings is highly nonnormal and state the null hypothesis.

A)H₀: M_d ≥ 100
B)H₀: M_d ≤ 100
C)H₀: M_d ≠ 100
D)H₀: M_d > 100

Question 69

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 pharmaceutical company that manufactures the drug wants to determine if the drug is helpful in reducing cholesterol levels.The cholesterol level readings are not normally distributed.State the alternative hypothesis for this problem.

A)The probability distribution of cholesterol readings of patients before and after taking the drug for six months is identical.
B)The probability distribution of cholesterol readings of patients after taking the drug has shifted to the left of the probability distribution of cholesterol readings of patients before taking the drug.
C)The probability distribution of cholesterol readings of patients after taking the drug has shifted to the right of the probability distribution of cholesterol readings of patients before taking the drug.
D)The probability distribution of cholesterol readings of patients after taking the drug has shifted to the right or left of the probability distribution of cholesterol readings of patients before taking the drug.

Question 70

An e-business/e-commerce information technology consulting company wants to compare the effectiveness of three programming languages that its programmers use.Currently each programming language is used by approximately 1/3 of the company's programmers.The director of the programming division randomly selected 5 programmers from the users of each of the three programming languages and assigned the same simple programming task to each programmer.All three populations have highly skewed distributions with extreme outliers.
The rank sum values for each of the programming groups are: T₁ = 23,T₂ = 48,and T₃ = 49.At α = .05,does the median time required to program a simple task differ between the three different programming languages?

A)H = 4.34,reject the null hypothesis.
B)H = 4.34,do not reject the null hypothesis.
C)H = 5.99,reject the null hypothesis.
D)H = 5.99,do not reject the null hypothesis.

Question 71

The EPA has stipulated that the Pollution Standard Index (PSI)for clean air standards is to average no more than 100.A random sample of 9 days for the city of Acorn showed PSI readings of 144,85,90,120,150,105,93,130,and 115.Assume the population of PSI readings is highly nonnormal.Is there significant evidence to conclude that Acorn's air is dirtier than the stipulated clean air standards? Test at α = .05.

A)Reject the null hypothesis.
B)Do not reject the null hypothesis.

Question 72

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?

A)Reject the null hypothesis,the diameter is greater for 1^st shift versus 2^nd 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 73

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.
State the alternative hypothesis.Assume that the population of starting salaries in marketing is not normally distributed.

A)H_A: M_d < 34,000
B)H_A: M_d > 34,000
C)H_A: M_d ≠ 34,000
D)H_A: M_d = 34,000

Question 74

Two NFL scouts are in the process of recruiting 7 college senior football players (receivers).After a careful review and evaluation,both scouts ranked the seven receivers in terms of their professional career prospects.If we want to determine whether the two scouts have similar opinions about the professional football career prospects of the seven players,state the null hypothesis.

A)H₀: ρ_s ≠ 0
B)H₀: ρ_s ≥ 0
C)H₀: ρ_s ≤ 0
D)H₀: ρ_s = 0

Question 75

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.The p value is found to be .0547.Using α = .10,can we conclude that the starting salaries increased in the last five years?

A)Yes
B)No

Question 76

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?

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

Question 77

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. $$\begin{array} { c c c } & { \text { Cholesterol level } } \\\text { Patient } & \text { Before } & \text { After } \\1 & 210 & 205 \\2 & 208 & 204 \\3 & 185 & 186 \\4 & 215 & 207 \\5 & 192 & 193 \\6 & 218 & 214 \\7 & 170 & 178 \\8 & 196 & 190 \\9 & 220 & 212 \\10 & 215 & 204\end{array}$$
)

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 78

Two NFL scouts are in the process of recruiting 7 college senior football players (receivers).After a careful review and evaluation,both scouts ranked the seven receivers in terms of their professional career prospects.The rankings are given below. $$\begin{array} { c c c } \begin{array} { c } \text { Player } \\\text { (Receiver) }\end{array} & \begin{array} { c } \text { Rankings of } \\\text { Scout } 1\end{array} & \begin{array} { c } \text { Rankings of } \\\text { Scout } 2\end{array} \\1 & 3 & 3 \\2 & 2 & 1 \\3 & 1 & 2 \\4 & 4 & 6 \\5 & 5 & 4 \\6 & 7 & 7 \\7 & 6 & 5\end{array}$$
At ? = .05,does it appear that the two scouts have similar opinions about the professional football career prospects of the seven players?

A)Reject the null hypothesis.
B)Do not reject the null hypothesis.
$$\begin{array} { c c c c c } \text { Receiver } & \text { Rankings of } & \text { Rcoutkings of } & d _ { i } & d _ { i } ^ { 2 } \\1 & 3 & \text { Scout } 2 & 3 & 0 \\2 & 2 & 1 & 1 & 1 \\3 & 1 & 2 & - 1 & 1 \\4 & 4 & 6 & - 2 & 4 \\5 & 5 & 4 & 1 & 1 \\6 & 7 & 7 & 0 & 0 \\7 & 6 & 5 & 1 & 1 \\& & & \text { Total } = & 8\end{array}$$
$$\begin{array} { l } \sum d _ { i } ^ { 2 } = 8 \\r _ { s } = 1 - \frac { 6 \sum d _ { i } ^ { 2 } } { n \left( n ^ { 2 } - 1 \right) } = 1 - \left[ \frac { ( 6 ) ( 8 ) } { 7 \left( 7 ^ { 2 } - 1 \right) } \right] = 1 - .1429 = .8571\end{array}$$

Question 79

An international economist believes that there is a significant relationship between the amount of debt and the rate of unemployment.He randomly selected six countries to determine if there is a significant relationship between debt and unemployment rate.In the following table,debt figures for the 6 countries are given in billions of dollars and the corresponding unemployment rate is given in percentages.He also discovered that both the distribution of debt and the distribution of unemployment rate were highly skewed.Use Spearman's rank correlation and determine if there is a significant correlation between debt and unemployment rate.Show the rank correlation. $$\begin{array} { c c c } && \text { Unemployment } \\\text { Country } & \text { Debt }& \text { Rate } \\1&1&5\\2 & 3 & 5 \\3 & 5 & 8 \\4 & 1 & 4 \\5 & 6 & 8 \\6 & 6 & 12\end{array}$$

A)r_s = .914,reject the null hypothesis.
B)r_s = .886,do not reject the null hypothesis.
C)r_s = .886,reject the null hypothesis.
D)r_s = .914,do not reject the null hypothesis.

Question 80

A manufacturer of cell phone batteries claims that the median life of a battery is more than 40 hours.Suppose a random sample of 75 batteries finds that 32 have a life of more than 40 hours.State the null hypothesis to test the claim.Assume that the population of all battery lives is not normally distributed.

A)H₀: M_d ≥ 40
B)H₀: M_d ≠ 40
C)H₀: M_d > 40
D)H₀: M_d ≤ 40