Question 1

Nonparametric methods are more sensitive than their parametric counterparts even when
the assumptions of the parametric methods are met.

Accepted Answer

A) True 
 B)False  True

Question 2

Two students were asked to rate six different television shows on a scale from 1 to 10 points, with higher values ranking ahead of lower values. Compute the sum of squares of the difference in ranks $\sum d ^ { 2 }$, as needed in a Spearman rank correlation coefficient.
$\begin{array}{c|cccccc}
\text { Show } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \
\hline \text { Student 1 } & 3 & 6 & 8 & 6 & 5 & 7 \
\text { Student 2 } & 7 & 9 & 3 & 5 & 2 & 5
\end{array}$

Accepted Answer

A)  41.5 
B)  3.0 
C)  0.0 
D)  33.5 
A)  41.5 
B)  3.0 
C)  0.0 
D)  33.5 A

Question 3

If a student is interested in determining whether or not a particular score was the median
grade on the statistics exam, he might ask several other students what their scores were
then apply the Wilcoxon rank sum test..

Accepted Answer

A) True 
 B)False  True

Question 4

A random sample of 12 men and 12 women were asked to report the number of hours they watched television on a Wednesday evening. If a researcher wants to test the hypothesis that there is no difference in the amount of time spent watching television based on gender, what $z$-values should be used for a two-tailed Wilcoxon rank sum test, at $\alpha = 0.05$ ?

Accepted Answer

A)  $z = \pm 2.00$ 
B)  $z = \pm 1.67$ 
C)  $z = \pm 3.00$ 
D)  $z = \pm 1.96$ 
A)  $z = \pm 2.00$ 
B)  $z = \pm 1.67$ 
C)  $z = \pm 3.00$ 
D)  $z = \pm 1.96$

Question 5

A researcher tests three different brands of $2 \%$ milk to see how many grams of fat are in e 8 ounce glass. The results are shown below.
$\begin{array}{ccc}
\hline \text { Brand A } & \text { Brand B } & \text { Brand C } \
\hline 4.76 & 4.72 & 4.78 \
4.74 & 4.75 & 4.76 \
4.72 & 4.76 & 4.79 \
4.79 & 4.74 & 4.77 \
4.75 & 4.77 & 4.78 \
\hline
\end{array}$

Find the sum of the ranks for Brand $C$.

Accepted Answer

A)  4.78 
B)  22.5 
C)  23.88 
D)  58 
A)  4.78 
B)  22.5 
C)  23.88 
D)  58

Question 6

Test the following sequence of values for randomness with respect to being above or belowthe median.
$\begin{array} { l l l l l l l l l l l l l l l } 4 & 6 & 3 & 8 & 5 & 9 & 5 & 7 & 3 & 7 & 9 & 1 & 3 & 8 & 6 \end{array}$
Table of Critical Values for the Number of Runs, $\alpha = 0.05$
$\begin{array}{c|cccc}
\text { Value of } & {\text { Value of } \boldsymbol{n}_{\mathbf{2}}} \
\boldsymbol{n}_{\mathbf{1}} & \mathbf{4} & \mathbf{5} & \mathbf{6} & \mathbf{7} \
\hline & 2 & 3 & 3 & 3 \
\mathbf{6} & 9 & 10 & 11 & 12 \
& 2 & 3 & 3 & 3 \
\mathbf{7} & 10 & 11 & 12 & 13 \
& 3 & 3 & 3 & 4 \
\mathbf{8} & 10 & 11 & 12 & 13
\end{array}$

Accepted Answer

A)  Do not reject the hypothesis that the sequence is random, because the test value 6 is between the critical values 3 and 13 
B)  Reject the hypothesis that the sequence is random, because the test value 6 is between the critical values 3 and 12 
C)  Reject the hypothesis that the sequence is random, because the test value 10 is between the critical values 3 and 13 
D)  Do not reject the hypothesis that the sequence is random, because the test value 10 is between the critical values 3 and 12 
A)  Do not reject the hypothesis that the sequence is random, because the test value 6 is between the critical values 3 and 13 
B)  Reject the hypothesis that the sequence is random, because the test value 6 is between the critical values 3 and 12 
C)  Reject the hypothesis that the sequence is random, because the test value 10 is between the critical values 3 and 13 
D)  Do not reject the hypothesis that the sequence is random, because the test value 10 is between the critical values 3 and 12

Question 7

_________statistics can be used to test hypotheses that do not involve specific population parameters such as $\mu , \sigma$, or $p$.

Accepted Answer

The answer of _________statistics can be used to test hypotheses...

Question 8

How many runs are in the following sequence? A A B A B B B B B A B A

Accepted Answer

A)  9 
B)  10 
C)  8 
D)  7 
A)  9 
B)  10 
C)  8 
D)  7

Question 9

A paired-sample sign test is used to test hypotheses comparing two dependent samples,
such as a before and after test.

Accepted Answer

A) True 
 B)False

Question 10

Two students rated, then ranked seven different television shows. The final rankings are listed in the table below. Determine the critical value needed for the Spearman rank correlation coefficient to reject the null hypothesis that the two students' rankings are not correlated at $\alpha = 0.01$.
$\begin{array}{c|ccccccc}
\text { Show } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } \
\hline \text { Student 1 } & 1 & 7 & 3 & 4 & 2 & 5 & 6 \
\text { Student 2 } & 3 & 6 & 1 & 5 & 4 & 2 & 7
\end{array}$

Accepted Answer

A)  0.929 
B)  0.780 
C)  0.716 
D)  1.000 
A)  0.929 
B)  0.780 
C)  0.716 
D)  1.000

Question 11

A researcher believes that the median lowest temperature for February is 25 degrees Fahrenheit. A random sample of 14 years yields the following lowest temperatures for Fel in degrees Fahrenheit:
$\begin{array} { l l l l l l l l l l l l l l } 10 & 10 & 12 & 14 & 14 & 16 & 17 & 19 & 20 & 22 & 25 & 27 & 31 & 33 \end{array}$
Test the researcher's hypothesis at $\alpha = 0.05$.
You may use the following abbreviated table of critical values (two tailed, $\alpha = 0.05$ ) from Table J:
$\begin{array}{l|ccccccccccccccc}
\mathbf{n} & \mathbf{1 1} & \mathbf{1 2} & \mathbf{1 3} & \mathbf{1 4} & \mathbf{1 5} & \mathbf{1 6} & \mathbf{1 7} & \mathbf{1 8} & \mathbf{1 9} & \mathbf{2 0} & \mathbf{2 1} & \mathbf{2 2} & \mathbf{2 3} & \mathbf{2 4} & \mathbf{2 5} \
\hline \text { critical value } & 1 & 2 & 2 & 3 & 3 & 3 & 4 & 4 & 4 & 5 & 5 & 5 & 6 & 6 & 6
\end{array}$

Accepted Answer

A)  Do not reject the claim because the test value 3 is equal to the critical value 
B)  Reject the claim because the test value 4 is more than the critical value 3. 
C)  Do not reject the claim because the test value 3 is more than the critical value 
D)  Reject the claim because the test value 4 is more than the critical value 2. 
A)  Do not reject the claim because the test value 3 is equal to the critical value 
B)  Reject the claim because the test value 4 is more than the critical value 3. 
C)  Do not reject the claim because the test value 3 is more than the critical value 
D)  Reject the claim because the test value 4 is more than the critical value 2.

Question 12

If a researcher using the sign test counts 15 positive signs and 8 negative signs, the test value is .

Accepted Answer

A)  -7 
B)  7 
C)  8 
D)  15 
A)  -7 
B)  7 
C)  8 
D)  15

Question 13

A researcher wished to compare the automobile color preferences of men and women. An experiment was performed recording the preferences of 6 men and 6 women. If the sum of squares of the ranking differences is equal to $12.1$, compute the Spearman rank correlation coefficient $r _ { s ^ { * } }$.

Accepted Answer

A)  0.428 
B)  0.958 
C)  0.654 
D)  0.809 
A)  0.428 
B)  0.958 
C)  0.654 
D)  0.809

Question 14

A researcher tests three different brands of $2 \%$ milk to see how many grams of fat are in e 8 ounce glass. The results are shown below.
$\begin{array}{ccc}
\hline \text { Brand A } & \text { Brand B } & \text { Brand C } \
\hline 4.72 & 4.68 & 4.74 \
4.70 & 4.71 & 4.72 \
4.68 & 4.72 & 4.75 \
4.75 & 4.70 & 4.73 \
4.71 & 4.73 & 4.74 \
\hline
\end{array}$

What is the critical value for a Kruskal-Wallis test of this data at $\alpha = 0.10$.

Accepted Answer

A)  6.251 
B)  4.605 
C)  0.584 
D)  0.211 
A)  6.251 
B)  4.605 
C)  0.584 
D)  0.211

Question 15

If the test value for a Wilcoxon signed-rank test $w _ { \mathrm { S } }$ is 15 , the sample size is 12 , and the one-tailed test is to be carried out at the $\alpha = 0.05$ level of significance, should the null hypothesis be rejected? Use the table of critical values for the signed-rank test below.

Accepted Answer

A)  Reject null hypothesis because the test value 15 is greater than the critical value 14 
B)  Do not reject null hypothesis because the test value 15 is less than the critical value 17 
C)  Do not reject null hypothesis because the test value 15 is greater than the critical value 14 
D)  Reject null hypothesis because the test value 15 is less than the critical value 17. 
A)  Reject null hypothesis because the test value 15 is greater than the critical value 14 
B)  Do not reject null hypothesis because the test value 15 is less than the critical value 17 
C)  Do not reject null hypothesis because the test value 15 is greater than the critical value 14 
D)  Reject null hypothesis because the test value 15 is less than the critical value 17.

Question 16

What is the critical value for a one-tailed sign test, at α = 0.01 when there are 14 samples?

Accepted Answer

A)  4 
B)  1 
C)  3 
D)  2 
A)  4 
B)  1 
C)  3 
D)  2

Question 17

If a researcher using the sign test has 15 positive signs and 22 negative signs in a test involving 37 samples, the $z$ test value is

Accepted Answer

A)  1.15 
B)  -1.15 
C)  1.32 
D)  -0.99 
A)  1.15 
B)  -1.15 
C)  1.32 
D)  -0.99

Question 18

An instructor divided her class into four groups and asked them to keep track of the number of soft drinks that they consume per week. In preparation for using the Kruskal-Wallis test to support or reject an hypothesis about the behavior of the different groups, combine and rank the following data. Find the sum of the ranks $f$ group.

$\begin{array}{l}
\text { Soft Drinks Consumed per Week }\
\begin{array}{c|c|c|c}
\text { Group A } & \text { Group B } & \text { Group C } & \text { Group D } \
\hline 7 & 4 & 2 & 3 \
10 & 20 & 5 & 9 \
14 & 6 & 13 & 16 \
12 & 11 & 15 & 17 \
8 & 9 & 10 & 18
\end{array}
\end{array}$

Accepted Answer

\[\begin{array} { c c c } 
\boldsymbol {

Question 19

A landscaping company hypothesizes that the median number of lawns they mow in a we 20. They tabulated the number of lawns mowed in a random sample of 14 weekends.
$\begin{array} { l l l l l l l } 22 & 18 & 19 & 20 & 25 & 20 & 18 \ 22 & 23 & 20 & 21 & 26 & 24 & 22 \end{array}$
What is the test value? d is

Accepted Answer

A)  7 
B)  8 
C)  4 
D)  3 
A)  7 
B)  8 
C)  4 
D)  3

Question 20

A landscaping company hypothesizes that the median number of lawns they mow weekend is 20 . They tabulated the number of lawns mowed in a random sample of weekends.
$\begin{array} { l l l l l l l } 22 & 18 & 19 & 20 & 25 & 20 & 18 \ 22 & 23 & 20 & 21 & 26 & 24 & 22 \end{array}$
State the null hypothesis.

Accepted Answer

@#LAT-DLM& : The median number

Nonparametric methods are more sensitive than their parametric counterparts even when the assumptions of the parametric methods are met.

If a student is interested in determining whether or not a particular score was the median grade on the statistics exam, he might ask several other students what their scores were then apply the Wilcoxon rank sum test..

A researcher tests three different brands of $2 \%$ milk to see how many grams of fat are in e 8 ounce glass. The results are shown below. Brand A Brand B Brand C 4.76 4.72 4.78 4.74 4.75 4.76 4.72 4.76 4.79 4.79 4.74 4.77 4.75 4.77 4.78 Find the sum of the ranks for Brand $C$ .

Test the following sequence of values for randomness with respect to being above or belowthe median. 4 6 3 8 5 9 5 7 3 7 9 1 3 8 6 Table of Critical Values for the Number of Runs, $\alpha = 0.05$ Value of Value of 2 3 3 3 9 10 11 12 2 3 3 3 10 11 12 13 3 3 3 4 10 11 12 13

_________statistics can be used to test hypotheses that do not involve specific population parameters such as $\mu , \sigma$ , or $p$ .

How many runs are in the following sequence? A A B A B B B B B A B A

A paired-sample sign test is used to test hypotheses comparing two dependent samples, such as a before and after test.

If a researcher using the sign test counts 15 positive signs and 8 negative signs, the test value is .

A researcher wished to compare the automobile color preferences of men and women. An experiment was performed recording the preferences of 6 men and 6 women. If the sum of squares of the ranking differences is equal to $12.1$ , compute the Spearman rank correlation coefficient $r _ { s ^ { * } }$ .

What is the critical value for a one-tailed sign test, at α = 0.01 when there are 14 samples?

If a researcher using the sign test has 15 positive signs and 22 negative signs in a test involving 37 samples, the $z$ test value is

A landscaping company hypothesizes that the median number of lawns they mow in a we 20. They tabulated the number of lawns mowed in a random sample of 14 weekends. 22 18 19 20 25 20 18 22 23 20 21 26 24 22 What is the test value? d is

A landscaping company hypothesizes that the median number of lawns they mow weekend is 20 . They tabulated the number of lawns mowed in a random sample of weekends. 22 18 19 20 25 20 18 22 23 20 21 26 24 22 State the null hypothesis.

The Nature of Probability and Statistics

Frequency Distributions and Graphs

Data Description

Probability and Counting Rules

Discrete Probability Distributions

The Normal Distribution

Confidence Intervals and Sample Size

Hypothesis Testing

Testing the Difference Between Two Means, Two Variances, and Two Proportions

Correlation and Regression

Other Chi-Square Tests

Analysis of Variance

Sampling and Simulation

Filters

Exam 13: Nonparametric Statistics

Nonparametric methods are more sensitive than their parametric counterparts even when the assumptions of the parametric methods are met.

If a student is interested in determining whether or not a particular score was the median grade on the statistics exam, he might ask several other students what their scores were then apply the Wilcoxon rank sum test..

A researcher tests three different brands of 2%2 \%2% milk to see how many grams of fat are in e 8 ounce glass. The results are shown below. Brand A Brand B Brand C 4.76 4.72 4.78 4.74 4.75 4.76 4.72 4.76 4.79 4.79 4.74 4.77 4.75 4.77 4.78 Find the sum of the ranks for Brand CCC .

Test the following sequence of values for randomness with respect to being above or belowthe median. 4 6 3 8 5 9 5 7 3 7 9 1 3 8 6 Table of Critical Values for the Number of Runs, α=0.05\alpha = 0.05α=0.05 Value of Value of 2 3 3 3 9 10 11 12 2 3 3 3 10 11 12 13 3 3 3 4 10 11 12 13

_________statistics can be used to test hypotheses that do not involve specific population parameters such as μ,σ\mu , \sigmaμ,σ , or ppp .

How many runs are in the following sequence? A A B A B B B B B A B A

A paired-sample sign test is used to test hypotheses comparing two dependent samples, such as a before and after test.

If a researcher using the sign test counts 15 positive signs and 8 negative signs, the test value is .

What is the critical value for a one-tailed sign test, at α = 0.01 when there are 14 samples?

If a researcher using the sign test has 15 positive signs and 22 negative signs in a test involving 37 samples, the zzz test value is

A landscaping company hypothesizes that the median number of lawns they mow in a we 20. They tabulated the number of lawns mowed in a random sample of 14 weekends. 22 18 19 20 25 20 18 22 23 20 21 26 24 22 What is the test value? d is

A landscaping company hypothesizes that the median number of lawns they mow weekend is 20 . They tabulated the number of lawns mowed in a random sample of weekends. 22 18 19 20 25 20 18 22 23 20 21 26 24 22 State the null hypothesis.

The Nature of Probability and Statistics

Frequency Distributions and Graphs

Data Description

Probability and Counting Rules

Discrete Probability Distributions

The Normal Distribution

Confidence Intervals and Sample Size

Hypothesis Testing

Testing the Difference Between Two Means, Two Variances, and Two Proportions

Correlation and Regression

Other Chi-Square Tests

Analysis of Variance

Sampling and Simulation

Filters

A researcher tests three different brands of $2 \%$ milk to see how many grams of fat are in e 8 ounce glass. The results are shown below. Brand A Brand B Brand C 4.76 4.72 4.78 4.74 4.75 4.76 4.72 4.76 4.79 4.79 4.74 4.77 4.75 4.77 4.78 Find the sum of the ranks for Brand $C$ .

Test the following sequence of values for randomness with respect to being above or belowthe median. 4 6 3 8 5 9 5 7 3 7 9 1 3 8 6 Table of Critical Values for the Number of Runs, $\alpha = 0.05$ Value of Value of 2 3 3 3 9 10 11 12 2 3 3 3 10 11 12 13 3 3 3 4 10 11 12 13

_________statistics can be used to test hypotheses that do not involve specific population parameters such as $\mu , \sigma$ , or $p$ .

If a researcher using the sign test has 15 positive signs and 22 negative signs in a test involving 37 samples, the $z$ test value is