Deck 13: Nonparametric Methods

Question 1

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

Answer 1

False

Question 2

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 comes from independent samples.
E)Nonparametric tests cannot be used if the same value appears in more than one data set being analyzed.

Answer 2

C

Question 3

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

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

Answer 3

A

Question 4

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

Question 5

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

Question 6

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 7

If the data set consists of matched pairs collected from two dependent populations then the Wilcoxon signed rank test may be appropriate to use.

Question 8

Nonparametric tests can be more powerful than the corresponding t or F tests if the population distribution is highly skewed or not normal.

Question 9

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 10

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

Question 11

An assumption of the Wilcoxon signed ranks test is that the samples are independent.

Question 12

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

Question 13

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

Question 14

The Wilcoxon signed rank test is a nonparametric test.

Question 15

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

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

Question 16

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

Question 17

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

Question 18

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 19

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

Question 20

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

A)Spearman's test
B)Sign test
C)Kruskall-Wallis test
D)Wilcoxon rank sum test
E)Friedman test

Question 21

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

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

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 rank test
B)Wilcoxon rank sum test
C)Sign test
D)Kruskall-Wallis test
E)Spearman's rank correlation test

Question 23

In a manufacturing facility producing fasteners,a supervisor suspects that the diameter of the bolt produced by the second shift workers is greater than the diameter of the bolts produced by the first shift workers.The supervisor takes a sample of 5 bolts from the first shift and a sample of 4 bolts from the second shift and measures the diameters.The distribution of bolt diameter measurements is not normally distributed.Which one of the following nonparametric tests is appropriate for this problem?

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

Question 24

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 25

The Wilcoxon signed rank 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 26

Refer to the Mega-Stat/Excel output for the Wilcoxon rank sum test given in the table below.
$\text { Wilcoxon - Mann/Whitney Test }$
$\begin{array} { l }\quad2\quad\quad\text { sum of ranks }\\\begin{array}{|c|c|}\hline 10\quad\quad \quad& 66.5\quad \\\hline 10 & 143.5 \\\hline \end{array}&\begin{array} { l }\text { Group } 1\\\text { Group } 2\\\end{array}\\\quad 20\quad\quad\quad\quad210&\text { total }\\\end{array}$

105.00 $\quad$ expected value
13.07 $\quad$ standard deviation
$-2.91\quad \mathrm{z}$ , corrected for ties
$.0037\quad \mathrm{p}$ -value (two-
tailed)

-At a significance level of .05,which one of the following rejection point conditions is correct when testing H₀: D₁ and D₂ have identical probability distributions versus H_a: D₁ is shifted to the right or left of D₂?

A)Reject H₀ if T ? 80 or T ? 46
B)Reject H₀ if T ? 127 or T ? 83
C)Reject H₀ if T ? 131 or T ? 79
D)Reject H₀ if T ? 111 or T ? 69
E)Reject H₀ if T ? 105 or T ? 66

Question 27

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

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

Question 28

Refer to the Mega-Stat/Excel output for the Wilcoxon rank sum test given in the table below.
$\text { Wilcoxon - Mann/Whitney Test }$
$\begin{array} { l }\quad2\quad\quad\text { sum of ranks }\\\begin{array}{|c|c|}\hline 10\quad\quad \quad& 66.5\quad \\\hline 10 & 143.5 \\\hline \end{array}&\begin{array} { l }\text { Group } 1\\\text { Group } 2\\\end{array}\\\quad 20\quad\quad\quad\quad210&\text { total }\\\end{array}$

105.00 $\quad$ expected value
13.07 $\quad$ standard deviation
$-2.91\quad \mathrm{z}$ , corrected for ties
$.0037\quad \mathrm{p}$ -value (two-
tailed)

-At a significance level of .05,which one of the following statements is correct when testing H₀: D₁ and D₂ have identical probability distributions versus H_a: D₁ is shifted to the right or left of D₂?

A)We reject H₀ and conclude there is very strong evidence that D₁ is shifted to the right or left of D₂.
B)We reject H₀ and conclude there is very strong evidence that D₁ is shifted to the left of D₂.
C)We failed to reject H₀ and conclude there is not sufficient evidence that D₁ is shifted to the left of D₂.
D)We failed to reject H₀ and conclude there is not sufficient evidence to conclude that D₁ and D₂ significantly differ in location.
E)We failed to reject H₀ and conclude there is very strong evidence that D₁ is shifted to the right D₂.

Question 29

Which one of the following nonparametric methods can be considered as an extension of the Wilcoxon rank sum test to three or more populations?

A)Wilcoxon signed rank test
B)Sign test
C)Kruskall-Wallis test
D)Spearman's test
E)Adcock Addition test

Question 30

Parametric methods are ____________ more powerful than their nonparametric counterparts.

A)always
B)sometimes
C)never

Question 31

The sign 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 32

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 is recorded for each patient.The distribution of cholesterol levels is not normally distributed.Which one of the following nonparametric tests is appropriate for this problem?

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

Question 33

Two professional football scouts are in the process of recruiting 7 new 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 be chosen?

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

Question 34

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 ¹ 7,then the p-value is:

A).0161
B).0029
C).0384
D).0322
E).0192

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 > 6,then the p-value is:

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

Question 36

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).0161
B).0729
C).0192
D).0384
E).1458

Question 37

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 38

The fire marshal has stipulated that the room capacity for a particular room is to be no more than 100 on the average.A random sample of the room's occupancy rate for 9 days had the following number of people: 144,85,90,120,150,105,93,130 and 115.Assume the population of room occupancy counts is not normal.The fire marshal wants to determine if there is significant evidence to conclude that the room has had more than 100 people on average.Which one of the following tests is appropriate for this problem?

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

Question 39

The __________________ is a general test to detect whether the probability distribution of one population has 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 rank test
D)Kruskall-Wallis test
E)Schermer Summation test

Question 40

Five years ago,the average starting salary of a new university 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 rank test
B)Wilcoxon rank sum test
C)Sign test
D)Kruskall-Wallis test
E)Mann-Whitney test

Question 41

What type of non-parametric statistic would generate the following excel/MegaStat output? 0 $\quad$$\quad$ sum of positive ranks
21 $\quad$$\quad$ sum of negative ranks
$\begin{array} { r l } 6 & n \\ 10.50 & \text { expected value } \\ 4.09 & \text { standard deviation } \\ - 2.57 & z \text {, corrected for ties } \\ .0103 & \text { p-value (two-tailed) } \end{array}$

A)Subtraction sigma test
B)Wilcoxon signed rank test
C)Sign test
D)Kruskall-Wallis test
E)Spearman's rank correlation test

Question 42

In a manufacturing facility producing fasteners,a supervisor suspects that the diameter of the bolt produced by the first shift workers is greater than the diameter of the bolts produced by the second shift workers.The supervisor takes a sample of 5 bolts from the first shift and a sample of 4 bolts from the second shift and measures the diameters.Below are the results from 5 first shift and 4 second shift observations.Distribution of bolt diameter measurements is not normally distributed.Given the data below,what is the value of T₂? $$\begin{array}{l}\text { Diameter of the bolts }\\\begin{array} { c c } 1 ^ { \text {st } } \text { shift } & 2 ^ { \text {nd } } \text { shift } \\2.01 & 1.80 \\2.25 & 1.95 \\1.98 & 2.30 \\2.05 & 2.00 \\2.03 &\end{array}\end{array}$$

A)16
B)29
C)8.05
D)10.32
E)22

Question 43

Consider the following pairs of observed values (x,y): (10,2), (8,3), (7,5), (5,4), (3,6), (2,9).Compute Spearman's rank correlation coefficient for this data set.

A)0.037
B)-0.744
C)-0.863
D)0.842
E)-0.943

Question 44

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

Question 45

Two professional football scouts (Sc)are in the process of recruiting 7 new 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. $$\begin{array} { c c c } \begin{array} { c } \text { Player } \\\text { (Receiver) }\end{array} & \text { Rankings of Sc. 1 } & \text { Rankings of Sc. 2 } \\1 & 3 & 3 \\2 & 2 & 1 \\3 & 1 & 2 \\4 & 4 & 6 \\5 & 5 & 4 \\6 & 7 & 7 \\7 & 6 & 5\end{array}$$
What is the value of d_i²?

A)0
B)2
C)6
D)8
E)10

Question 46

A professional organization is attempting to determine whether salaries of hospital CFO s differ by geographical region. Five hospital CFOs were randomly selected from each of the following four regions: Maritimes, Quebec, Ontario, and Western Canada. Each CFO was then asked their annual salary. The distributions of salaries were highly skewed. The table below summarizes the results of the Kruskal-Wallis test obtained from Mega-Stat/Excel.
$$\begin{array}{l}\text { Kruskal-Wallis Test }\\\begin{array} { c c c } \hline \text { Median } & n & \begin{array} { c } \text { Avg. } \\\text { Rank }\end{array} \\\hline 59.00 & 5 & 17.20 \text { Group 1 } \\55.30 & 5 & 10.40 \text { Group 2 } \\54.10 & 5 & 9.10 \text { Group 3 } \\53.20 & 5 & 5.30 \text { Group } 4 \\\hline 55.70 & 20 & \text { Total } \\\hline & & 10.565 \text { H (corrected for ties) } \\& & 3 \text { d.f. } \\& & .0143 \text { p-value }\end{array}\end{array}$$

-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 appeared that the bivariate normal probability distribution assumption is 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 47

A professional organization is attempting to determine whether salaries of hospital CFO s differ by geographical region. Five hospital CFOs were randomly selected from each of the following four regions: Maritimes, Quebec, Ontario, and Western Canada. Each CFO was then asked their annual salary. The distributions of salaries were highly skewed. The table below summarizes the results of the Kruskal-Wallis test obtained from Mega-Stat/Excel.
$$\begin{array}{l}\text { Kruskal-Wallis Test }\\\begin{array} { c c c } \hline \text { Median } & n & \begin{array} { c } \text { Avg. } \\\text { Rank }\end{array} \\\hline 59.00 & 5 & 17.20 \text { Group 1 } \\55.30 & 5 & 10.40 \text { Group 2 } \\54.10 & 5 & 9.10 \text { Group 3 } \\53.20 & 5 & 5.30 \text { Group } 4 \\\hline 55.70 & 20 & \text { Total } \\\hline & & 10.565 \text { H (corrected for ties) } \\& & 3 \text { d.f. } \\& & .0143 \text { p-value }\end{array}\end{array}$$

-At a significance level of .05,the rejection point condition for the hypothesis test is:

A)Reject H₀ if c² > 9.3484
B)Reject H₀ if c² > 30.1435
C)Reject H₀ if c² > 7.81473
D)Reject H₀ if c² > .341846
E)Reject H₀ if c² > 32.8523

Question 48

Refer to the Mega-Stat/Excel output for the Wilcoxon rank sum test given in the table below.
$\text { Wilcoxon - Mann/Whitney Test }$
$\begin{array} { l }\quad2\quad\quad\text { sum of ranks }\\\begin{array}{|c|c|}\hline 10\quad\quad \quad& 66.5\quad \\\hline 10 & 143.5 \\\hline \end{array}&\begin{array} { l }\text { Group } 1\\\text { Group } 2\\\end{array}\\\quad 20\quad\quad\quad\quad210&\text { total }\\\end{array}$

105.00 $\quad$ expected value
13.07 $\quad$ standard deviation
$-2.91\quad \mathrm{z}$ , corrected for ties
$.0018\quad \mathrm{p}$ -value (two-
tailed)

-At a significance level of .05,which one of the following statements is correct when the alternative hypothesis is H_a: D₁ is shifted to the left of D₂?

A)We reject H₀ and conclude there is very strong evidence that D₁ is shifted to the right or left of D₂.
B)We reject H₀ and conclude there is very strong evidence that D₁ is shifted to the left of D₂.
C)We failed to reject H₀ and conclude there is not sufficient evidence that D₁ is shifted to the left of D₂.
D)We failed to reject H₀ and conclude there is not sufficient evidence to conclude that D₁ is not shifted to the right or left of D₂.
E)We failed to reject H₀ and conclude there is very strong evidence that D₁ is shifted to the left of D₂.

Question 49

What type of non-parametric statistic would generate the following excel/MegaStat output? $\begin{array} { l }&\quad\quad\quad\quad\quad\quad\text { Unemployment }\\&\text { Debt }\quad\text { rate }\\\begin{array} { l } \text {Debt }\\\text { Unemployment}\\\text { rate}\\\end{array}&\begin{array}{|r|r|}\hline 1.000 \quad&\quad\quad\quad\quad \\\hline & \\.914 & 1.000 \\\hline\end{array}\end{array}$


$\begin{array}{r}6 &\text {sample size }\\\pm .811 &\text {critical value .05 (two-tail) }\\\pm .917&\text { critical value .01 (two-tail)}\end{array}$

A)Subtraction sigma test
B)Wilcoxon signed rank test
C)Sign test
D)Kruskall-Wallis test
E)Spearman's rank correlation test

Question 50

What type of non-parametric statistic would generate the following excel/MegaStat output? 3.5 $\quad$$\quad$ hypothesized value
6 $\quad$$\quad$ median
0 $\quad$$\quad$ below
0 $\quad$$\quad$ equal
7 $\quad$$\quad$ above
$7 \quad\quad\quad\mathrm { n }$
$\quad$$\quad$$\quad$ binomial
$.0078 \quad\mathrm { p }$ -value (one-tailed, upper)

A)Subtraction sigma test
B)Wilcoxon signed rank test
C)Sign test
D)Kruskall-Wallis test
E)Spearman's rank correlation test

Question 51

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 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.The value of T_i (rank sum)for Program A is _____. $$\begin{array} { c c c } \text { Program A } & \text { Program B } & \text { Program C } \\9 & 14 & 12 \\10 & 11 & 16 \\7 & 8 & 7 \\6 & 9 & 10 \\8 & 15 & 13\end{array}$$

A)40
B)48
C)23
D)49
E)57

Question 52

Refer to the Mega-Stat/Excel output for the Wilcoxon rank sum test given in the table below.
$\text { Wilcoxon - Mann/Whitney Test }$
$\begin{array} { l }\quad2\quad\quad\text { sum of ranks }\\\begin{array}{|c|c|}\hline 10\quad\quad \quad& 66.5\quad \\\hline 10 & 143.5 \\\hline \end{array}&\begin{array} { l }\text { Group } 1\\\text { Group } 2\\\end{array}\\\quad 20\quad\quad\quad\quad210&\text { total }\\\end{array}$

105.00 $\quad$ expected value
13.07 $\quad$ standard deviation
$-2.91\quad \mathrm{z}$ , corrected for ties
$.0018\quad \mathrm{p}$ -value (two-
tailed)

-At a significance level of .05,which one of the following rejection point conditions is correct when the alternative hypothesis is 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 53

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

Question 54

Two coffee-vending machines are studied to determine whether they distribute the same amounts.Samples are taken and the amounts dispensed are recorded for each machine.What is the value of T_B? $$\begin{array} { c c } \text { Machine A } & \text { Machine B } \\610 & 5.99 \\5.95 & 6.01 \\5.98 & 5.98 \\6.01 & 5.96 \\6.00 & 6.08 \\5.95 & 5.89 \\6.02 & 6.01 \\6.04 & 6.00 \\5.99 & 5.97 \\6.06 & 6.00\end{array}$$

A)117
B)122
C)93
D)59
E)119

Question 55

A professional organization is attempting to determine whether salaries of hospital CFO s differ by geographical region. Five hospital CFOs were randomly selected from each of the following four regions: Maritimes, Quebec, Ontario, and Western Canada. Each CFO was then asked their annual salary. The distributions of salaries were highly skewed. The table below summarizes the results of the Kruskal-Wallis test obtained from Mega-Stat/Excel.
$$\begin{array}{l}\text { Kruskal-Wallis Test }\\\begin{array} { c c c } \hline \text { Median } & n & \begin{array} { c } \text { Avg. } \\\text { Rank }\end{array} \\\hline 59.00 & 5 & 17.20 \text { Group 1 } \\55.30 & 5 & 10.40 \text { Group 2 } \\54.10 & 5 & 9.10 \text { Group 3 } \\53.20 & 5 & 5.30 \text { Group } 4 \\\hline 55.70 & 20 & \text { Total } \\\hline & & 10.565 \text { H (corrected for ties) } \\& & 3 \text { d.f. } \\& & .0143 \text { p-value }\end{array}\end{array}$$

-Wax-com Electronics Inc.claims that a certain circuit board has a median operating life of greater 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.Is there evidence to support their claim? What is the resulting test statistic and conclusion?

A)1.6,fail to reject H₀
B)1.6,reject H₀
C)-1.6,reject H₀
D)-1.6,fail to reject H₀
E)1.645,reject H₀

Question 56

Refer to the Mega-Stat/Excel output for the Wilcoxon signed rank test given in the table below.
Wilcoxon Signed Rank Test
variables: Group 1 - Group 2
5.5 sum of positive
ranks
30.5 sum of negative
ranks
$8 \quad\quad\mathrm { n }$
18.00 $\quad$ expected value
5.74 $\quad$ standard deviation
$- 2.18\quad \mathrm { z }$ , corrected for ties
.0296 $\quad$ p-value (two-
$\quad$$\quad$$\quad$ tailed)

-Assuming there were no paired differences equal to zero,at a significance level of .01 which one of the following rejection point conditions is correct when the alternative hypothesis is H_a: D₁ is shifted to the left of D₂?

A)T^- ? 5
B)T⁺ ? 0
C)T^- ? 11
D)T^- ? 3
E)Smaller of the T⁺ or T^- is less than 8

Question 57

Refer to the Mega-Stat/Excel output for the Wilcoxon signed rank test given in the table below.
Wilcoxon Signed Rank Test
variables: Group 1 - Group 2
5.5 sum of positive
ranks
30.5 sum of negative
ranks
$8 \quad\quad\mathrm { n }$
18.00 $\quad$ expected value
5.74 $\quad$ standard deviation
$- 2.18\quad \mathrm { z }$ , corrected for ties
.0296 $\quad$ p-value (two-
$\quad$$\quad$$\quad$ tailed)

-At a significance level of .01,which one of the following statements is correct when the alternative hypothesis is 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 failed to 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 58

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

Question 59

A professional organization is attempting to determine whether salaries of hospital CFO s differ by geographical region. Five hospital CFOs were randomly selected from each of the following four regions: Maritimes, Quebec, Ontario, and Western Canada. Each CFO was then asked their annual salary. The distributions of salaries were highly skewed. The table below summarizes the results of the Kruskal-Wallis test obtained from Mega-Stat/Excel.
$$\begin{array}{l}\text { Kruskal-Wallis Test }\\\begin{array} { c c c } \hline \text { Median } & n & \begin{array} { c } \text { Avg. } \\\text { Rank }\end{array} \\\hline 59.00 & 5 & 17.20 \text { Group 1 } \\55.30 & 5 & 10.40 \text { Group 2 } \\54.10 & 5 & 9.10 \text { Group 3 } \\53.20 & 5 & 5.30 \text { Group } 4 \\\hline 55.70 & 20 & \text { Total } \\\hline & & 10.565 \text { H (corrected for ties) } \\& & 3 \text { d.f. } \\& & .0143 \text { p-value }\end{array}\end{array}$$

-At a significance level of .05,which one of the following statements is correct regarding the null hypothesis H₀: The distributions of CFO salaries are identical for all four regions?

A)We reject H₀ and conclude there is very strong evidence that the distributions of CFO salaries differ in location for all four regions.
B)We failed to reject H₀ and conclude there is not sufficient evidence that the distributions of CFO salaries differ significantly in location any of the four regions.
C)We failed to reject H₀ and conclude there is only adequate evidence that the median hospital CFO salaries differ between at least two of the four regions.
D)We reject H₀ and conclude there is strong evidence that the distributions of CFO salaries differ in location between at least two of the four regions.
E)We failed to reject H₀ and conclude that the distributions of CFO salaries are identical for all four regions.

Question 60

The claim of the manufacturer of cell phone batteries is 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.Does the evidence support their claim? Which is the corresponding test statistic result?

A)-1.39
B)1.96
C)-1.96
D)1.39
E)1.55

Question 61

Five years ago, the average starting salary of a new university 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 population of starting salaries in marketing is not normally distributed.
The local university wants to determine if the median starting salary for marketing graduates has increased in the last five years.


-Using a = .05,can we conclude that the starting salaries increased in the last five years?

Question 62

Wax-com Electronics Inc. claims that a certain circuit board has a median operating life of greater 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. Is there evidence to support their claim?

-State the null and alternative hypotheses.

Question 63

Based on this result of the test,provide a one sentence conclusion.

Question 64

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 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.

-Calculate the value of T_i (rank sum)for each of the three samples.

Question 65

A copy machine service company provides maintenance and repair service for different types and brands of copiers.The manager of the repair department wants to know if the repair time for brand A is higher than the repair time for brand B.The manager randomly selected 8 repair records associated with brand A and 8 repair records associated with brand B.The repair times for both samples in minutes are given below.The distribution of repair times for both brand A and brand B is highly skewed.
What is the appropriate null and alternative hypothesis for this problem?

Question 66

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

Question 67

Five years ago, the average starting salary of a new university 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 population of starting salaries in marketing is not normally distributed.
The local university wants to determine if the median starting salary for marketing graduates has increased in the last five years.


-State the null and alternative hypotheses.

Question 68

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.

Question 69

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

Question 70

Are repair times for brand A systematically higher than the repair times for brand B? Test at a = .05.
B.H₀: D_A and D_B are identical,H_A: D_A is shifted to the right of D_B
T = 89.5
From table A15 for n₁ = 8,and n₂ = 8,T_U = 84
Since 89.5 > 84,we reject H₀ and conclude that the repair times for brand A is higher than the repair times for brand

Question 71

A packaging company of dog biscuits has stipulated that the number of dog biscuits per package is to be no more than 100 on the average. A random sample of 9 packages had the following number of biscuits: 144, 85, 90, 120, 150, 105, 93, 130 and 115. Assume the population of biscuit counts per package is non-normal. The company wants to test to determine if more biscuits are going into each package than the stipulated 100.

-Is there significant evidence to conclude that more biscuits are going into each package than the stipulated 100? Test at a = .05.

Question 72

A packaging company of dog biscuits has stipulated that the number of dog biscuits per package is to be no more than 100 on the average. A random sample of 9 packages had the following number of biscuits: 144, 85, 90, 120, 150, 105, 93, 130 and 115. Assume the population of biscuit counts per package is non-normal. The company wants to test to determine if more biscuits are going into each package than the stipulated 100.

-State the null and alternative hypothesis.

Question 73

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

Question 74

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.

Question 75

Wax-com Electronics Inc. claims that a certain circuit board has a median operating life of greater 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. Is there evidence to support their claim?

-At a = 0.05,can it be concluded that the sample supports their claim of the company? Assume the useful life of the circuit board is not normally distributed.

Question 76

Five years ago, the average starting salary of a new university 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 population of starting salaries in marketing is not normally distributed.
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 a = .10,can we conclude that the starting salaries have increased in the last five years?

Question 77

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,sum of the ranks for each of the p samples are calculated.

Question 78

If there are five or more observations in each sample,the Kruskall-Wallis H statistic has an approximately _____________ distribution.

Question 79

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

Question 80

The rank sum values for each of the programming groups are: T₁ = 23,T₂ = 48,and T₃ = 49.At a = .05,does the distribution of time required to program a simple task differ in location between at least one pair of programming languages?