Question 1

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.

Accepted Answer

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

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

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:

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 4

A nonparametric method that is equivalent to the Wilcoxon rank sum test is the:

Accepted Answer

The nonparametric method that is equivalent to the Wilcoxon rank sum test is the Mann-Whitney test. The Wilcoxon signed rank sum test is used for paired samples, the Friedman test is used for three or more related samples, and the Kruskal-Wallis test is used for three or more independent samples.

Question 5

In testing the hypotheses H₀: The two population locations are the same. H₁: The location of population A is to the left of the location of population b.The statistics n_A = 6,T_A = 32,n_B = 8,and T_B = 58 are calculated with data drawn from two independent samples: a.Which test is used for testing the hypotheses above? b.What is the p-value of this test?

Accepted Answer

The answer of In testing the hypotheses H₀: The two population...

Question 6

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

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

Question 7

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.

Accepted Answer

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

Question 8

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?

Accepted Answer

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

Question 9

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 10

Nonparametric procedures are often called ____________________-free statistics.

Accepted Answer

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

Question 11

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 12

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 indeed used for matched pairs when the data are ordinal and not necessarily normally distributed.

Question 13

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

Accepted Answer

The sign test and the t-test are both statistical tests that have their own advantages and disadvantages. The sign test is generally used for non-parametric data where the distribution is unknown or not normal, while the t-test is used for parametric data where the data is normally distributed. Therefore, the choice between the two tests depends on the nature of the data and the objective of the analysis. Hence, it cannot be said that the sign test is always preferred over the t-test.

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: 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:

Accepted Answer

Rank is assigned based on the order of the values from smallest to largest. The given data set can be ordered as follows: 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. The three observations of value 2.8 have ranks 7, 8, and 9, respectively. Therefore, the rank assigned to the three observations of value 2.8 is 8. The best choice is C, which corresponds to the rank of 8.

Question 16

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:

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 17

In testing the hypotheses H₀: The two population locations are the same. H₁: The two population locations are different. The critical values and sample sizes are n₁ = 5,T_L = 22,n₂ = 9,and T_U = 53. a.Which test is used for testing the hypotheses above? b.What is the α-level of this test?

Accepted Answer

The answer of In testing the hypotheses H₀: The two population...

Question 18

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 sign test does not have a strict requirement that the number of nonzero differences (n) must be greater than or equal to 30. It can be used with smaller sample sizes, although larger samples can provide more reliable results.

Question 19

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 20

Nonparametric methods are designed to test ____________________ data.

Accepted Answer

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

Quiz 19: Nonparametric Statistics