Question 1

-What is the test statistic T?

Accepted Answer

T = 117
T

Question 2

Calculate T- and T+

Accepted Answer

T^- = 38.5 and T⁺ = 6.5 T^- is sum

Question 3

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 supervisor 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 one 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 and alternative hypothesis for this problem.

Accepted Answer

H₀ :D_Trained and D_Untrained are ident

Question 4

On the average,can it be concluded that Internet purchases are significantly less than electronics store purchases? Test at $\alpha$ 
= .05
Can reject H0,so we have evidence that the distribution of Internet prices are shifted to the left of that of local electronics stores
T = 190

Accepted Answer

From the Wilcoxon Rank Sum tab

Question 5

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?

Accepted Answer

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. 
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 6

Calculate the value of TI and TE.

Accepted Answer

Question 7

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

Question 8

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

Accepted Answer

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

Question 9

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 Ha: D1 is shifted to the right or left of D2?

Accepted Answer

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. 
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 10

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

Accepted Answer

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

Question 11

Parametric methods are ____________ more powerful than their nonparametric counterparts.

Accepted Answer

A) always 
B) sometimes 
C) never 
A) always 
B) sometimes 
C) never

Question 12

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 13

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?

Accepted Answer

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

Question 14

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

Accepted Answer

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 
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 15

Given the following sample data: .980,1.01,.970,.990,1.00,1.00,.980,.970,.980,and .999,run a sign test on H0: Md = 1.00 with a 2-sided alternative at $\alpha$ = .05.

Accepted Answer

Fail to reject H₀ Num

Question 16

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

Accepted Answer

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 
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 17

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

Accepted Answer

A) True 
 B)False

Question 18

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 19

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
$\begin{array} { r l } 6 & n \ 10.50 & \text { expected value } \ 4.09 & \text { standard deviation } \ - 2.57 & z \text {, corrected for ties } \ .0103 & \text { p-value (two-tailed) } \end{array}$

Accepted Answer

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

Question 20

Using α = .05,can we conclude that the battery life is more than 40 hours?

Accepted Answer

Failed to reject H₀,so we can't

-What is the test statistic T?

Calculate T^- and T⁺

On the average,can it be concluded that Internet purchases are significantly less than electronics store purchases? Test at $\alpha$ = .05 Can reject H₀,so we have evidence that the distribution of Internet prices are shifted to the left of that of local electronics stores T = 190

Calculate the value of T_I and T_E.

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

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

Parametric methods are ____________ more powerful than their nonparametric counterparts.

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.

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

Given 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 $\alpha$ = .05.

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

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

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:

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 6 n 10.50 expected value 4.09 standard deviation -2.57 z , corrected for ties .0103 p-value (two-tailed)

Using α = .05,can we conclude that the battery life is more than 40 hours?

An Introduction to Business Statistics

Descriptive Statistics

Probability

Discrete Random Variables

Continuous Random Variables

Sampling Distributions

Confidence Intervals

Hypothesis Testing

Statistical Inferences Based on Two Samples

Experimental Design and Analysis of Variance

Correlation Coefficient and Simple Linear Regression Analysis

Multiple Regression and Model Building

Chi-Square Tests

Decision Theory

Time Series Forecasting

Filters

Exam 13: Nonparametric Methods

-What is the test statistic T?

Calculate T- and T+

On the average,can it be concluded that Internet purchases are significantly less than electronics store purchases? Test at α\alphaα = .05 Can reject H0,so we have evidence that the distribution of Internet prices are shifted to the left of that of local electronics stores T = 190

Calculate the value of TI and TE.

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

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

Parametric methods are ____________ more powerful than their nonparametric counterparts.

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.

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

Given the following sample data: .980,1.01,.970,.990,1.00,1.00,.980,.970,.980,and .999,run a sign test on H0: Md = 1.00 with a 2-sided alternative at α\alphaα = .05.

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

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

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:

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 6 n 10.50 expected value 4.09 standard deviation -2.57 z , corrected for ties .0103 p-value (two-tailed)

Using α = .05,can we conclude that the battery life is more than 40 hours?

An Introduction to Business Statistics

Descriptive Statistics

Probability

Discrete Random Variables

Continuous Random Variables

Sampling Distributions

Confidence Intervals

Hypothesis Testing

Statistical Inferences Based on Two Samples

Experimental Design and Analysis of Variance

Correlation Coefficient and Simple Linear Regression Analysis

Multiple Regression and Model Building

Chi-Square Tests

Decision Theory

Time Series Forecasting

Filters

Calculate T^- and T⁺

On the average,can it be concluded that Internet purchases are significantly less than electronics store purchases? Test at $\alpha$ = .05 Can reject H₀,so we have evidence that the distribution of Internet prices are shifted to the left of that of local electronics stores T = 190

Calculate the value of T_I and T_E.

Given 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 $\alpha$ = .05.

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:

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 6 n 10.50 expected value 4.09 standard deviation -2.57 z , corrected for ties .0103 p-value (two-tailed)