Question 1

The Friedman test is employed to compare two or more populations when the data are generated from a matched pairs experiment, and are either ordinal or interval but not normally distributed.

Accepted Answer

The Friedman test is a non-parametric test used to compare two or more populations that are related through a matched pairs experiment, and the data should be either ordinal or interval but not necessarily normally distributed.

Question 2

Use the 5% significance level to test the hypotheses. $H _ { 0 } :$ The two population locations are the same $H _ { 1 } :$ The location of population A is to the left of the location of population B,
given that the data below are drawn from a matched pairs experiment. $\begin{array} { | c | c | c | c | c | c | c | c | c | } 
\hline \text { Matched Pair } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \
\hline \text { A } & 8 & 10 & 11 & 7 & 6 & 7 & 13 & 10 \
\hline \text { B } & 6 & 9 & 12 & 10 & 12 & 10 & 5 & 8 \
\hline
\end{array}$

Accepted Answer

The answer of Use the 5% significance level to test...

Question 3

We can use the Friedman test to determine whether a difference exists between two populations. However, if we want to determine whether one population location is larger than another, we must use the sign test.

Accepted Answer

The answer of We can use the Friedman test to...

Question 4

We can use the Friedman test to determine whether two populations differ. The conclusion will be the same as that produced by the sign test.

Accepted Answer

The Friedman test is a non-parametric test used to compare three or more related samples. It is typically used when the data is not normally distributed or when the variances are not equal. The sign test, on the other hand, is a non-parametric test used to compare two related samples. Therefore, the two tests are meant for different purposes, and the conclusion produced by each test may not necessarily be the same.

Question 5

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 suitable for non-parametric data, such as ordinal data, and is often used for matched pairs designs. Normal distribution is not a requirement for the use of the sign test.

Question 6

In a normal approximation to the sign test, the standardised test statistic is calculated as z = 2.07. If the alternative hypothesis states that the location of population 1 is to the right of the location of population 2, then the p-value of the test is 0.0192.

Accepted Answer

In a normal approximation to the sign test with alternative hypothesis stating that population 1 is to the right of population 2, a positive z-value gives a p-value less than 0.5. A z-value of 2.07 corresponds to a p-value of 0.0192, which is less than 0.5. Therefore, the statement is true.

Question 7

The Wilcoxon rank sum test is used to compare two populations when the samples are independent and the data are either ordinal or interval but not normally distributed.

Accepted Answer

The Wilcoxon rank sum test, also known as the Mann-Whitney U test, is used to compare two independent populations when the data are not normally distributed and can be ordinal or interval.

Question 8

The Kruskal-Wallis test can be used to test for a difference between two populations. It will produce the same outcome as the two-tailed Wilcoxon rank sum test.

Accepted Answer

The Kruskal-Wallis test is a non-parametric alternative to the one-way ANOVA test, and it can be used to test for differences among more than two populations. However, when comparing only two populations, the Kruskal-Wallis test produces the same outcome as the two-tailed Wilcoxon rank sum test.

Question 9

A Wilcoxon rank sum test for comparing two independent samples involves two samples of sizes 5 and 8. The alternative hypothesis is that the location of population 1 is different from the location of population 2. Using the 0.10 significance level, the appropriate critical values are 21 and 49.

Accepted Answer

The answer of A Wilcoxon rank sum test for comparing...

Question 10

The Kruskal-Wallis test is applied to compare two or more populations when the samples are independent and the data are ordinal or numerical and non-normal.

Accepted Answer

The description accurately describes the Kruskal-Wallis test.

Question 11

Given the following statistics from a matched pairs experiment, perform the Wilcoxon signed rank sum test to determine whether we can infer at the 10% significance level that the two population locations differ. $T ^ { + } = 520$ $T ^ { - } = 700$ , n = 50

Accepted Answer

The answer of Given the following statistics from a matched...

Question 12

The Kruskal-Wallis test can be used to determine whether a difference exists between two populations. However, to determine whether one population location is larger than another, we must apply the Wilcoxon rank sum test.

Accepted Answer

The answer of The Kruskal-Wallis test can be used to...

Question 13

The Wilcoxon signed rank sum test is applied to compare two populations when the samples are matched pairs and the data are interval but not normally distributed.

Accepted Answer

The Wilcoxon signed rank sum test is a nonparametric test that is used to compare two populations when the sample data are not normally distributed and the variables are paired.

Question 14

The Kruskal-Wallis test uses the Chi-squared distribution.

Accepted Answer

The Kruskal-Wallis test is a non-parametric test used to compare three or more independent groups. It ranks the values within each group and uses the sum of ranks as the test statistic. The test is based on the assumption that the shape of the distribution is similar across all groups. The Kruskal-Wallis test follows a Chi-squared distribution with (k-1) degrees of freedom, where k is the number of groups being compared. Therefore, the statement "The Kruskal-Wallis test uses the Chi-squared distribution" is true.

Question 15

In a normal approximation to the Wilcoxon rank sum test, the standardised test statistic is calculated as z = 1.96. For a two-tailed test, the p-value is 0.025.

Accepted Answer

The answer of In a normal approximation to the Wilcoxon...

Question 16

A Wilcoxon rank sum test for comparing two independent samples involves two samples of sizes 6 and 9. The alternative hypothesis is that the location of population 1 is to the left of the location of population 2. Using the 0.05 significance level, the appropriate critical values are 31 and 65.

Accepted Answer

The answer of A Wilcoxon rank sum test for comparing...

Question 17

A Wilcoxon rank sum test for comparing two populations involves two independent samples of sizes 15 and 20. The value of the unstandardised test statistic is T = 225. The value of the standardised test statistic is z = -1.50.

Accepted Answer

The answer of A Wilcoxon rank sum test for comparing...

Question 18

One of the required conditions of the sign test is that the number of nonzero differences n must be smaller than or equal to 10.

Accepted Answer

This statement is false. The number of nonzero differences can be any positive integer, there is no limitation on the value.

Question 19

In a Wilcoxon rank sum test for independent samples, the two sample sizes are 4 and 6, and the value of the Wilcoxon test statistic is T = 25. If the test is two-tailed and the level of significance is 0.05, then the null hypothesis will be rejected.

Accepted Answer

The answer of In a Wilcoxon rank sum test for...

Question 20

Radio advertising is big business, second only to television advertising. The objective for radio advertisements is to get listeners to remember as much as possible about the product/service being advertised. The advertising executive of a large company must decide between two pitched radio advertisements for their company. In order to ascertain the general public's perception, 12 randomly chosen people are selected to listen to both potential advertisements and are then asked a series of 5 questions regarding the radio advertisement's content. The number of correct responses are recorded and listed below. Assume that responses are non-normal. $\text { Number of correct responses from } 10 \text { questions }$
$\begin{array}{|c|c|c|}
\hline \text { Respondent } & \begin{array}{c}
\text { Radio } \
\text { advertisement 1 }
\end{array} & \begin{array}{c}
\text { Radio } \
\text { advertisement 2 }
\end{array} \
\hline 1 & 3 & 1 \
\hline 2 & 5 & 5 \
\hline 3 & 5 & 4 \
\hline 4 & 4 & 3 \
\hline 5 & 3 & 2 \
\hline 6 & 2 & 1 \
\hline 7 & 1 & 3 \
\hline 8 & 4 & 2 \
\hline 9 & 5 & 1 \
\hline 10 & 3 & 4 \
\hline 11 & 4 & 3 \
\hline 12 & 3 & 1 \
\hline
\end{array}$ a. Which test is appropriate for this situation?
b. Do these data provide enough evidence at the 5% significance level to conclude that the two radio advertisements differ?

Accepted Answer

The answer of Radio advertising is big business, second only...

Quiz 21: Nonparametric Techniques

The Friedman test is employed to compare two or more populations when the data are generated from a matched pairs experiment, and are either ordinal or interval but not normally distributed.

We can use the Friedman test to determine whether a difference exists between two populations. However, if we want to determine whether one population location is larger than another, we must use the sign test.

We can use the Friedman test to determine whether two populations differ. The conclusion will be the same as that produced by the sign test.

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.

In a normal approximation to the sign test, the standardised test statistic is calculated as z = 2.07. If the alternative hypothesis states that the location of population 1 is to the right of the location of population 2, then the p-value of the test is 0.0192.

The Wilcoxon rank sum test is used to compare two populations when the samples are independent and the data are either ordinal or interval but not normally distributed.

The Kruskal-Wallis test can be used to test for a difference between two populations. It will produce the same outcome as the two-tailed Wilcoxon rank sum test.

A Wilcoxon rank sum test for comparing two independent samples involves two samples of sizes 5 and 8. The alternative hypothesis is that the location of population 1 is different from the location of population 2. Using the 0.10 significance level, the appropriate critical values are 21 and 49.

The Kruskal-Wallis test is applied to compare two or more populations when the samples are independent and the data are ordinal or numerical and non-normal.

Given the following statistics from a matched pairs experiment, perform the Wilcoxon signed rank sum test to determine whether we can infer at the 10% significance level that the two population locations differ. T+=520T ^ { + } = 520T+=520 T−=700T ^ { - } = 700T−=700 , n = 50

The Kruskal-Wallis test can be used to determine whether a difference exists between two populations. However, to determine whether one population location is larger than another, we must apply the Wilcoxon rank sum test.

The Wilcoxon signed rank sum test is applied to compare two populations when the samples are matched pairs and the data are interval but not normally distributed.

The Kruskal-Wallis test uses the Chi-squared distribution.

In a normal approximation to the Wilcoxon rank sum test, the standardised test statistic is calculated as z = 1.96. For a two-tailed test, the p-value is 0.025.

A Wilcoxon rank sum test for comparing two independent samples involves two samples of sizes 6 and 9. The alternative hypothesis is that the location of population 1 is to the left of the location of population 2. Using the 0.05 significance level, the appropriate critical values are 31 and 65.

A Wilcoxon rank sum test for comparing two populations involves two independent samples of sizes 15 and 20. The value of the unstandardised test statistic is T = 225. The value of the standardised test statistic is z = -1.50.

One of the required conditions of the sign test is that the number of nonzero differences n must be smaller than or equal to 10.

In a Wilcoxon rank sum test for independent samples, the two sample sizes are 4 and 6, and the value of the Wilcoxon test statistic is T = 25. If the test is two-tailed and the level of significance is 0.05, then the null hypothesis will be rejected.

Given the following statistics from a matched pairs experiment, perform the Wilcoxon signed rank sum test to determine whether we can infer at the 10% significance level that the two population locations differ. $T ^ { + } = 520$ $T ^ { - } = 700$ , n = 50