Question 1

The sign test is always to be preferred to the t-test.

Accepted Answer

The statement is not accurate. The sign test is appropriate for non-parametric data, while the t-test should be used for parametric data. Therefore, the choice between these two tests depends on the nature and distribution of the data being analyzed.

Question 2

When the sample sizes from both populations are larger than ____________________,the Wilcoxon rank sum statistic has an approximate normal distribution.

Accepted Answer

The answer of When the sample sizes from both populations...

Question 3

When the sample sizes from both populations are larger than 10,the Wilcoxon rank sum statistic has an approximate ____________________ distribution.

Accepted Answer

The answer of When the sample sizes from both populations...

Question 4

Consider the following data set: 2.2,2.3,2.3,2.5,2.6,2.7,2.8,2.8,2.8,2.9,3.1,3.2,and 3.5.The rank assigned to the three observations of value 2.8 is:
A) 6
B) 7
C) 8
D) 9

Accepted Answer

The rank of an observation is its position in the ordered list of all the observations. 
So, first we arrange the data set in ascending order: 
2.2, 2.3, 2.3, 2.5, 2.6, 2.7, 2.8, 2.8, 2.8, 2.9, 3.1, 3.2, 3.5 
Then we assign ranks to each observation starting from 1 for the smallest observation and increasing by 1 for each subsequent observation. 
The three observations of value 2.8 are the 7th, 8th, and 9th observations in the ordered list. Therefore, they receive ranks of 7, 8, and 9, respectively. Hence the best choice is C.

Question 5

Comparing the output of strawberries grown on plots using fertilizer A with that grown on otherwise identical plots using fertilizer B,in order to make a general assessment of relative fertilizer effectiveness,may well call for a:
A) Friedman test.
B) Kruskal-Wallis test.
C) Wilcoxon rank-sum test.
D) Spearman rank correlation test.

Accepted Answer

The Wilcoxon rank-sum test is appropriate for comparing the outputs (e.g., yield, size, quality) of strawberries grown on two different plots using different fertilizers when the data are not normally distributed. This test is used to assess whether there is a significant difference between two independent samples, which aligns with the scenario of comparing the effectiveness of two fertilizers.

Question 6

Nonparametric procedures are often called ____________________-free statistics.

Accepted Answer

The answer of Nonparametric procedures are often called ____________________-free statistics....

Question 7

A nonparametric method that is equivalent to the Wilcoxon rank sum test is the:
A) Wilcoxon signed rank sum test.
B) Friedman test.
C) Kruskal-Wallis test.
D) Mann-Whitney test.

Accepted Answer

The Wilcoxon rank sum test is also known as the Mann-Whitney test, making choice D the correct answer. The other nonparametric methods mentioned (Wilcoxon signed rank sum test, Friedman test, and Kruskal-Wallis test) are all different tests that serve different purposes and are not equivalent to the Wilcoxon rank sum test.

Question 8

H₀ in the Wilcoxon rank sum test is that the two population ____________________ are the same.

Accepted Answer

The answer of H₀ in the Wilcoxon rank sum test...

Question 9

Because of the rising costs of construction accidents many construction firms have instituted safety courses.Employees are encouraged to take these courses designed to heighten safety awareness.A company is trying to decide which one of two courses to institute.To help make a decision,eight employees take course 1 and another eight take course 2.Each employee writes a test,which is marked,out of a possible 25.The results are shown below.Does this data provide sufficient evidence at the 5% level of significance to conclude that the marks from course 2 are higher than those of course 1? Assume that the scores are not normally distributed.
 $$\begin{array}{l}
\text { Safaty Tast scores }\
\begin{array} { | c c | } 
\hline \text { Course 1 } & \text { Caurse 2 } \
\hline 14 & 20 \
21 & 18 \
17 & 22 \
14 & 15 \
17 & 23 \
19 & 21 \
20 & 19 \
16 & 15 \
\hline
\end{array}
\end{array}$$

Accepted Answer

The answer of Because of the rising costs of construction...

Question 10

Nonparametric methods are designed to test ____________________ data.

Accepted Answer

The answer of Nonparametric methods are designed to test ____________________...

Question 11

Use the Wilcoxon rank sum test on the data below to determine at the 5% significance level whether the location of population A is to the left of the location of population B.
 $$\begin{array} { l l l r r r } 
\text { Sannple A: } & 75 & 60 & 67 & 54 & 69 \
\text { Sangle } B : & 80 & 84 & 100 & 74 & 90
\end{array}$$

Accepted Answer

The answer of Use the Wilcoxon rank sum test on...

Question 12

The Wilcoxon rank sum test requires that the samples from the two populations be ____________________.

Accepted Answer

The answer of The Wilcoxon rank sum test requires that...

Question 13

Each year the human resources department in a large corporation assesses the performance of all of its employees.Each employee is rated for various aspects of his or her job on a 7-point scale where 1 = very unsatisfactory and 7 = satisfactory.The CEO of the company believes that the assessment scores this year are lower than last year's.To examine the validity of this belief she draws a random sample of six employees' scores from last year and another six employees' scores this year.Do the data listed below allow the CEO to conclude at the 5% significance level that her belief is correct?
 $$\begin{array}{l}
\text { Employess Ratingr Feores }\
\begin{array} { | c c | } 
\hline \text { This Year } & \text { Last Year } \
\hline 5 & 5 \
6 & 5 \
4 & 3 \
5 & 3 \
5 & 4 \
4 & 3 \
\hline
\end{array}
\end{array}$$

Accepted Answer

The answer of Each year the human resources department in...

Question 14

Instead of testing whether population means differ,a nonparametric technique would test whether the population ____________________ differ.

Accepted Answer

The answer of Instead of testing whether population means differ,a...

Question 15

Consider the following data set: 14,14,15,16,18,19,19,20,21,22,23,25,25,25,25,and 28.The rank assigned to the four observations of value 25 is:
A) 12
B) 12.5
C) 13
D) 13.5

Accepted Answer

In ranking, when multiple observations have the same value, they are assigned the average of the ranks they would have occupied if they were slightly different. The four observations of value 25 are the 11th, 12th, 13th, and 14th in the ordered list. The average of these ranks is (11+12+13+14)/4 = 50/4 = 12.5. However, since ranking starts at 1, not 0, we adjust this to start from the first position, making the correct rank 13.5.

Question 16

A two-sample t-test is the parametric counterpart of the Wilcoxon signed rank sum test for matched pairs.

Accepted Answer

A two-sample t-test is the parametric counterpart of the Wilcoxon rank sum test (also known as the Mann-Whitney U test) for independent samples. The Wilcoxon signed rank sum test is the non-parametric counterpart of the paired t-test.

Question 17

The sign test is employed to compare two populations when the experimental design is matched pairs,and the data are ordinal but not normally distributed.

Accepted Answer

The sign test is used when we have non-parametric data, which means the data is not normally distributed. It is also used in a matched pairs design where each observation in one sample is paired with an observation in the other sample. Finally, the sign test is appropriate for ordinal data because it only looks at the direction of the differences and not the magnitude, which is appropriate for ordinal data.

Question 18

In the Wilcoxon rank sum test statistic,let T represent the total rankings of sample 1 amongst all rankings.If T is small,this suggests that the location of population 1 is to the ____________________ of the location of population 2.

Accepted Answer

The answer of In the Wilcoxon rank sum test statistic,let...

Question 19

A two independent sample t-test corresponds to a Wilcoxon signed rank sum test for paired samples.

Accepted Answer

A two independent sample t-test compares the means of two separate groups, while a Wilcoxon signed rank sum test compares the medians of two paired samples. Therefore, they are not equivalent and cannot be substituted for each other.

Question 20

One of the required conditions of the sign test is that the number of nonzero differences n must be greater than or equal to 30.

Accepted Answer

The required condition for the sign test is that the number of observations n must be greater than or equal to 20. There is no specific requirement for the number of nonzero differences.

Quiz 19: Nonparametric Statistics