Question 1

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 < 16,then the p-value is:

Accepted Answer

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

Question 2

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.
-State the null and alternative hypotheses to test the claim.Assume that the population of all battery lives is not normally distributed.

Accepted Answer

H₀:M_d ? 40 v

Question 3

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

Accepted Answer

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 
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 4

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.

Accepted Answer

Failed to reject H₀ H₀:M_d @#IMG-DLM& 20,00

Question 5

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.The rankings are given below.

Accepted Answer

@#IMG-DLM& 
At @#IMG-DLM& 
= .05,does it appear that the two

Question 6

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?

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 7

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

Accepted Answer

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

Question 8

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.

Accepted Answer

H₀:M_d ? 34,0

Question 9

What is the rejection point T0 for $\alpha$ = .05?

Accepted Answer

T₀ = 8 (n =

Question 10

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. $$\begin{array} { c c } 
\text { Machine A } & \text { Machine B } \
\hline 610 & 5.99 \
610 & 5.99 \
5.95 & 6.01 \
5.98 & 5.98 \
6.01 & 5.96 \
6.00 & 6.08 \
5.95 & 5.89 \
6.02 & 6.01 \
6.04 & 6.00 \
5.99 & 5.97 \
6.06 & 6.00
\end{array}$$
-What is the appropriate null and alternative hypotheses for the claim that they distribute the same amount of coffee?

Accepted Answer

H₀:D_A and D_B are identi

Question 11

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.

Accepted Answer

H₀:M_d ? 100

Question 12

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

Accepted Answer

A) True 
 B)False

Question 13

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?

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

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

Accepted Answer

A) True 
 B)False

Question 15

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

Accepted Answer

Wilcoxon s

Question 16

Three years ago,a major hotel chain purchased a large number of heating and air-conditioning units from three major manufacturers,A,B and
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 $\alpha$ = .05,can it be concluded that there is a significant difference in repair costs among the three brands? $$\begin{array} { l c c } 
\text { Brand A } & \text { Brand B } & \text { Brand C } \
\$ 80 & \$ 100 & \$ 140 \
\$ 250 & \$ 170 & \$ 280 \
\$ 150 & \$ 430 & \$ 100 \
\$ 70 & \$ 290 & \$ 100 \
\$ 220 & \$ 370 & \$ 340 \
\$ 300 & \$ 420 & \$ 250 \
& \$ 350 &
\end{array}$$ Failed to reject H0.No significant difference in location of the distribution of cost between the three brands. $\begin{array}{lrcrcr}
\text { Brand A } & \left(\mathrm{R}_{\mathrm{A}}\right) & \text { Brand B } & \left(\mathrm{R}_{\mathrm{B}}\right) & \text { Brand C } & \left(\mathrm{R}_{\mathrm{C}}\right) \
\$ 80 & (2) & \$ 100 & (4) & \$ 140 & (6) \
\$ 250 & (10.5) & \$ 170 & (8) & \$ 280 & (12) \
\$ 150 & (7) & \$ 430 & (19) & \$ 100 & (4)\
\$ 70 & (1) & \$ 290 & (13) & \$ 100 & (4) \
\$ 220 & (9) & \$ 370 & (17) & \$ 340 & (15) \
\$ 300 & (14) & \$ 420 & (18) & \$ 250 & (10.5)\
&43.5&\$350&(16)&&51.5\&&&95
\end{array}$ TA = 43.5TB = 95TC = 51.5 $$\begin{array} { l } 
\chi _ { .05,2 } ^ { 2 } = 5.99 \
H = \frac { 12 } { ( 19 ) ( 20 ) } \left[ \frac { ( 43.5 ) ^ { 2 } } { 6 } + \frac { ( 95 ) ^ { 2 } } { 7 } + \frac { ( 51.5 ) ^ { 2 } } { 6 } \right] - 3 ( 19 + 1 ) \
H = 4.633 \
4.633 < 5.99 , \text { failed to reject } H _ { 0 }
\end{array}$$ There is no significant difference in location of the distribution of cost between the three brands.

Accepted Answer

@#IMG-DLM& 
= .05,can it be concluded that there i

Question 17

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 is given below.Distribution of cholesterol level is not normally distributed.At a = .05,test to determine if the drug is helpful in reducing cholesterol levels.

Accepted Answer

@#IMG-DLM& Reject H₀ H₀:The probability distributio

Question 18

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.

Accepted Answer

@#IMG-DLM& 
At @#IMG-DLM& 
= .05,can we conclude that the su

Question 19

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.

Accepted Answer

H₀:M_d @#IMG-DLM& 20,0

Question 20

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? $$\begin{array}{l}
\text { Diameter of the bolts }\
\begin{array} { c c } 
1 ^ { \text {st } } \text { shift } & 2 ^ { \text {nd } } \text { shift } \
2.01 & 1.80 \
2.25 & 1.95 \
1.98 & 2.30 \
2.05 & 2.00 \
2.03 &
\end{array}
\end{array}$$

Accepted Answer

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

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:

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.The rankings are given below.

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

What is the rejection point T₀ for $\alpha$ = .05?

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

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

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

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

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 < 16,then the p-value is:

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.The rankings are given below.

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

What is the rejection point T0 for α\alphaα = .05?

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

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

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

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

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:

What is the rejection point T₀ for $\alpha$ = .05?