Question 1

A researcher wants to determine whether the means of two independent populations are the same.She has two independent random samples, one from each population, shown in the following table:  $\quad $ $\quad $ $\quad $ $\quad $Sample I $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $Sample II
$\begin{array}{llll|lllll}
\hline 11.5 & 15.7 & 22.8 & 22.5 & 12.6 & 13.8 & 17.5 & 10.7 & 13.5 \
12.4 & 25.3 & 16.1 & 25.1 & 14.8 & 11.8 & 14.7 & 10.8 & 12.7
\end{array}$

She uses the Mann-Whitney U test and a significance level of 0.05.The appropriate
Decision is ______.

Accepted Answer

A) reject the null hypothesis that the two populations have different means 
B) fail to reject the null hypothesis that the two populations have different means 
C) reject the null hypothesis that the two populations have equal means 
D) fail to reject the null hypothesis that the two populations have equal means 
E) do nothing

Question 2

A production run of 500 items resulted in 29 defectives items.A defective item is coded as 1 and a good item as 0.The following is an output from Minitab. 
Runs Test: Defects

Runs test for Defects

Runs above and below $\mathrm { K } = 0.058$

The observed number of runs $= 57$
The expected number of runs $= 55.636$
29 observations above K, 471 below
$\mathrm { P } -$ value $= 0.574$
Using $\alpha$=0.1, the conclusion is __________________.

Accepted Answer

A) successive items did not constitute a random sample. 
B) reject the hypothesis that successive items constituted a random sample 
C) do not reject the hypothesis that successive items constituted a random sample 
D) reject the hypothesis that successive items constituted a random sample. 
E) the distribution is binomial

Question 3

The Mann-Whitney U test is implemented differently for small samples than for large samples.

Accepted Answer

A) True 
 B)False

Question 4

A researcher wants to determine the efficacy of a training program directed at improving concentration, focus, and memory on college students.She selects a random sample of 16 individuals and has them take an initial assessment test before the training program.Then the individuals complete the training program, and at the end they take a final test that's comparable to the initial test.The results are shown in the following table: $$\begin{array} { | c | c | c | } 
\hline \text { Individ. } & \text { Before } & \text { After } \
\hline 1 & 79 & 81 \
\hline 2 & 74 & 73 \
\hline 3 & 81 & 82.5 \
\hline 4 & 75 & 82.5 \
\hline 5 & 72.5 & 85 \
\hline 6 & 75 & 90 \
\hline 7 & 67.5 & 83.5 \
\hline 8 & 57.5 & 72.5 \
\hline 9 & 62.5 & 87.5 \
\hline 10 & 77.5 & 80 \
\hline 11 & 61.5 & 92.5 \
\hline 12 & 57.5 & 80 \
\hline 13 & 61.5 & 71 \
\hline 14 & 72.5 & 84 \
\hline 15 & 64 & 78.5 \
\hline 16 & 71 & 97.5 \
\hline
\end{array}$$ The analyst uses a Wilcoxon matched-pairs signed rank test with a 0.05 significance level.The observed z score is ______.

Accepted Answer

A) -3.4645 
B) -3.2157 
C) -3.0178 
D) -2.9857 
E) -2.7978

Question 5

Many "Before and after" types of experiments should be analyzed using _______.

Accepted Answer

A) chi-square goodness of fit test 
B) Kruskal-Wallis test 
C) Mann-Whitney U test 
D) Wilcoxon test 
E) Friedman test

Question 6

The nonparametric counterpart of the t test to compare the means of two related samples is the _______.

Accepted Answer

A) chi-square goodness of fit test 
B) chi-square test of independence 
C) Mann-Whitney U test 
D) Wilcoxon test 
E) Friedman test

Question 7

Spearman rank correlation values, rs, range between +1 and 0.

Accepted Answer

A) True 
 B)False

Question 8

The Wilcoxon test was used on 16 pairs of data.The total of the ranks (T)were computed to be 76 (for + ranks)and 60 (for - ranks).The z value for this test is _____.

Accepted Answer

A) -0.41 
B) -0.02 
C) 0.02 
D) 16 
E) -0.041.

Question 9

A researcher wants to determine the efficacy of a training program directed at improving concentration, focus, and memory on college students.She selects a random sample of 16 individuals and has them take an initial assessment test before the training program.Then the individuals complete the training program, and at the end they take a final test that's comparable to the initial test.The results are shown in the following table: $$\begin{array} { | c | c | c | } 
\hline \text { Individ. } & \text { Before } & \text { After } \
\hline 1 & 79 & 81 \
\hline 2 & 74 & 73 \
\hline 3 & 81 & 82.5 \
\hline 4 & 75 & 82.5 \
\hline 5 & 72.5 & 85 \
\hline 6 & 75 & 90 \
\hline 7 & 67.5 & 83.5 \
\hline 8 & 57.5 & 72.5 \
\hline 9 & 62.5 & 87.5 \
\hline 10 & 77.5 & 80 \
\hline 11 & 61.5 & 92.5 \
\hline 12 & 57.5 & 80 \
\hline 13 & 61.5 & 71 \
\hline 14 & 72.5 & 84 \
\hline 15 & 64 & 78.5 \
\hline 16 & 71 & 97.5 \
\hline
\end{array}$$ The analyst uses a Wilcoxon matched-pairs signed rank test with a 0.05 significance level.The appropriate decision is ______.

Accepted Answer

A) fail to reject the null hypothesis that the before and after scores are different 
B) reject the null hypothesis that that the before and after scores are different 
C) fail to reject the null hypothesis that the before and after scores are not different 
D) reject the null hypothesis that the before and after scores are not different 
E) do nothing

Question 10

A local pediatrician office is interested in the 'no-show' appointment count for each of the 4 pediatricians.'No-show' appointments represent lost revenues because the physician will be
Idle when patients do not show for their scheduled appointments.Using the data in the table
Below and an alpha of 0.10, what is the appropriate decision?
$$\begin{array} { r r r r r } 
& \text { Physician A } & \text { Physiciaan B } & \text { Physician C } & \text { Physician D } \
\text { week 1 } & 8 & 4 & 6 & 7 \
\text { week 2 } & 7 & 3 & 4 & 6 \
\text { week 3 } & 8 & 2 & 5 & 4 \
\text { week 4 } & 8 & 6 & 7 & 9 \
\text { week 5 } & 4 & 2 & 5 & 10
\end{array}$$
 $$\begin{array} { r r r r r } 
& \text { Physician A } & \text { Physician B } & \text { Physician C } & \text { Physician D } \
\text { week 1 } & 8 & 4 & 6 & 7 \
\text { week 2 } & 7 & 3 & 4 & 6 \
\text { week 3 } & 8 & 2 & 5 & 4 \
\text { week 4 } & 8 & 6 & 7 & 9 \
\text { week 5 } & 4 & 2 & 5 & 10
\end{array}$$

Accepted Answer

A) Reject the null hypothesis and conclude at least one physician differs in the no-show rates. 
B) Reject the null hypothesis and conclude the no show rates differ by day of week 
C) Fail to reject the null hypothesis and conclude there is not enough evidence to demonstrate the no show rate between physician is equal 
D) Fail to reject the null hypothesis and conclude there is not enough evidence to show the no show rate between days of the week is equal 
E) Reject the null hypothesis and conclude the no show rates are dependent upon both day of week and physician.

Question 11

The nonparametric alternative to analysis of variance for a randomized block design is the Friedman test.

Accepted Answer

A) True 
 B)False

Question 12

A researcher wants to determine whether the means of two independent populations are the same.She has two independent random samples, one from each population, shown in the following table:  $\quad $ $\quad $ $\quad $ $\quad $Sample I $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $Sample II
$\begin{array}{llll|lllll}
\hline 11.5 & 15.7 & 22.8 & 22.5 & 12.6 & 13.8 & 17.5 & 10.7 & 13.5 \
12.4 & 25.3 & 16.1 & 25.1 & 14.8 & 11.8 & 14.7 & 10.8 & 12.7
\end{array}$

She uses the Mann-Whitney U test and a significance level of 0.05.Then $\mu$U is ______.

Accepted Answer

A) 10.055 
B) 11.025 
C) 11.255 
D) 12.025 
E) 12.255

Question 13

A researcher wants to study the effects of physical exercise on depression.She randomly selects a group of 24 individuals who are equally depressed.None of these individuals currently exercises.She then randomly assigns them in one of three groups: group 1 stays without exercising (sedentary group), group 2 exercises once a week, and group 3 exercises two times a week.Individuals in groups 2 and 3 meet with a personal trainer so they carry out a very similar exercising program, both in kinds of exercises and in intensity.After two months, the researcher has all individuals take a depression-assessment test.The score of the test goes from 0 = totally miserable to 100 = complete satisfaction. The scores are shown in the following table:
$$\begin{array} { | c c c | } 
\hline \text { Group 1 } & \text { Group 2 } & \text { Group } 3 \
\hline 25 & 24 & 35 \
15 & 16 & 22 \
20 & 19 & 31 \
17 & 24 & 32 \
23 & 25 & 31 \
21 & 25 & 29 \
19 & 21 & 33 \
18 & 18 & 35 \
\hline
\end{array}$$ The researcher uses a Kruskal-Wallis test and a significance level $\alpha$= 0.05.The relevant number of degrees of freedom is ______.

Accepted Answer

A) 1 
B) 2 
C) 3 
D) 23 
E) 24

Question 14

A researcher wants to study the effects of physical exercise on depression.She randomly selects a group of 24 individuals who are equally depressed.None of these individuals currently exercises.She then randomly assigns them in one of three groups: group 1 stays without exercising (sedentary group), group 2 exercises once a week, and group 3 exercises two times a week.Individuals in groups 2 and 3 meet with a personal trainer so they carry out a very similar exercising program, both in kinds of exercises and in intensity.After two months, the researcher has all individuals take a depression-assessment test.The score of the test goes from 0 = totally miserable to 100 = complete satisfaction. The scores are shown in the following table:
$$\begin{array} { | c c c | } 
\hline \text { Group 1 } & \text { Group 2 } & \text { Group } 3 \
\hline 25 & 24 & 35 \
15 & 16 & 22 \
20 & 19 & 31 \
17 & 24 & 32 \
23 & 25 & 31 \
21 & 25 & 29 \
19 & 21 & 33 \
18 & 18 & 35 \
\hline
\end{array}$$ The researcher uses a Kruskal-Wallis test and a significance level $\alpha$ = 0.05.The appropriate decision is ______.

Accepted Answer

A) fail to reject the null hypothesis that the three groups have different levels of depression 
B) reject the null hypothesis that the three groups have different levels of depression 
C) fail to reject the null hypothesis that the three groups have equal levels of depression 
D) reject the null hypothesis that the three groups have equal levels of depression 
E) fail to reject the null hypothesis that the sample is random

Question 15

To compare the means of two populations which cannot be assumed to be normally distributed and only ordinal-level data is available from two independent samples, The Mann-Whitney U test should be used instead of the t-test for independent samples..

Accepted Answer

A) True 
 B)False

Question 16

The nonparametric counterpart of the t test to compare the means of two independent populations is the Mann-Whitney U test.

Accepted Answer

A) True 
 B)False

Question 17

Performance records for 18 salespersons are selected to investigate whether compensation methods are a significant motivational factor. $\begin{array}{lc}\
 \text { Compensation Method } \quad\quad\text { Sales }\
\begin{array}{|l|l|l|l|l|l|l|l|}
\hline \text { Straight Salary } & 18 & 12 & 22 & 28 & 28 & & \
\hline \text { Straight Commission } & 27 & 34 & 34 & 27 & 20 & 16 & 24 \
\hline \text { Salary plus Commission } & 11 & 17 & 27 & 14 & 30 & 22 & \
\hline
\end{array}\end{array}$
 A Kruskal-Wallis test is to be performed with $\alpha$ = 0.01.The calculated K value is _______.

Accepted Answer

A) 15.086 
B) 1.715 
C) 7.779 
D) 9.210 
E) 8.657

Question 18

The nonparametric alternative to analysis of variance for a randomized block design is the _______.

Accepted Answer

A) chi-square test 
B) Kruskal-Wallis test 
C) Mann-Whitney U test 
D) Wilcoxon test 
E) Friedman test

Question 19

A researcher wants to determine whether the means of two independent populations are the same.She has two independent random samples, one from each population, shown in the following table:  $\quad $ $\quad $ $\quad $ $\quad $Sample I $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $Sample II
$\begin{array}{llll|lllll}
\hline 11.5 & 15.7 & 22.8 & 22.5 & 12.6 & 13.8 & 17.5 & 10.7 & 13.5 \
12.4 & 25.3 & 16.1 & 25.1 & 14.8 & 11.8 & 14.7 & 10.8 & 12.7
\end{array}$
 She uses the Mann-Whitney U test and a significance level of 0.05.The sum of ranks for sample I is ______.

Accepted Answer

A) 99 
B) 101 
C) 102 
D) 104 
E) 106

Question 20

The methods of parametric statistics require ________________.

Accepted Answer

A) interval or ratio data 
B) nominal or ordinal data 
C) large samples 
D) small samples 
E) qualitative data

Exam 17: Nonparametric Statistics

The Mann-Whitney U test is implemented differently for small samples than for large samples.

Many "Before and after" types of experiments should be analyzed using _______.

The nonparametric counterpart of the t test to compare the means of two related samples is the _______.

Spearman rank correlation values, r_s, range between +1 and 0.

The Wilcoxon test was used on 16 pairs of data.The total of the ranks (T) were computed to be 76 (for + ranks) and 60 (for - ranks) .The z value for this test is _____.

The nonparametric alternative to analysis of variance for a randomized block design is the Friedman test.

To compare the means of two populations which cannot be assumed to be normally distributed and only ordinal-level data is available from two independent samples, The Mann-Whitney U test should be used instead of the t-test for independent samples..

The nonparametric counterpart of the t test to compare the means of two independent populations is the Mann-Whitney U test.

The nonparametric alternative to analysis of variance for a randomized block design is the _______.

The methods of parametric statistics require ________________.