Question 1

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

Accepted Answer

A) True 
 B)False

Question 2

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 Ti (rank sum)for each of the three samples.

Accepted Answer

@#IMG-DLM& T₁ = 23,T

Question 3

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 Ha: D1 is shifted to the left of D2?

Accepted Answer

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

Question 4

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

Accepted Answer

The answer of The Spearman's rank correlation test can be...

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}$$
-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?

Accepted Answer

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 
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 6

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

Accepted Answer

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 
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 7

The claim of a local real estate agent is that the median selling price of homes in a major city is more than $200,000. Suppose a random sample of 100 homes sold in the last six months is taken and 53 sold for over $200,000.
-State the null and alternative hypotheses to test the claim.Assume that the population of selling prices is not normally distributed.

Accepted Answer

H₀:M_d ? 2000

Question 8

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

Accepted Answer

The answer of If there are five or more observations...

Question 9

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

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

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 10

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?

Accepted Answer

The answer of Five years ago, the average starting salary...

Question 11

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.

Accepted Answer

A) sign test 
B) Wilcoxon rank sum test 
C) Wilcoxon signed rank test 
D) Kruskall-Wallis test 
E) Schermer Summation test 
A) sign test 
B) Wilcoxon rank sum test 
C) Wilcoxon signed rank test 
D) Kruskall-Wallis test 
E) Schermer Summation test

Question 12

Calculate the value of TA and TB

Accepted Answer

Question 13

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

Accepted Answer

A) True 
 B)False

Question 14

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. $$\begin{array} { l l l l l l l l l } 
\text { Brand A } & 160 & 159 & 171 & 155 & 136 & 128 & 173 & 143 \
\text { Brand B } & 125 & 160 & 140 & 131 & 119 & 123 & 135 & 134
\end{array}$$
-What is the appropriate null and alternative hypothesis for this problem?

Accepted Answer

H₀:D_A and D_B are identi

Question 15

-What is the test statistic T?

Accepted Answer

T = 190
T

Question 16

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:

Accepted Answer

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 
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 17

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 non-normal 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 hypotheses for this problem.

Accepted Answer

H₀:The probability distribution of writte

Question 18

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

Accepted Answer

The answer of If the population from which we sample...

Question 19

An international economist believes that there is a significant relationship between the amount of debt and the rate of unemployment.The economist 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.The economist 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.

Accepted Answer

@#IMG-DLM& Reject H₀.There appears to be significa

Question 20

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

Accepted Answer

A) True 
 B)False

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

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

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

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

What type of non-parametric statistic would generate the following excel/MegaStat output? Unemployment Debt rate Debt Unemployment rate 1.000 .914 1.000 6 sample size \pm.811 critical value .05 (two-tail) \pm.917 critical value .01 (two-tail)

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.

Calculate the value of T_A and T_B

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

-What is the test statistic T?

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

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

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

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

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

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

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

What type of non-parametric statistic would generate the following excel/MegaStat output? Unemployment Debt rate Debt Unemployment rate 1.000 .914 1.000 6 sample size \pm.811 critical value .05 (two-tail) \pm.917 critical value .01 (two-tail)

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.

Calculate the value of TA and TB

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

-What is the test statistic T?

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

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

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 the value of T_A and T_B