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Chapter 13: Q1BSC (page 597)

Sign Test for Freshman 15 The table below lists some of the weights (kg) from Data Set 6 “Freshman 15” in Appendix B. Those weights were measured from college students in September and later in April of their freshman year. Assume that we plan to use the sign test to test the claim of no difference between September weights and April weights. What requirements must be satisfied for this test? Is there any requirement that the populations must have a normal distribution or any other specific distribution? In what sense is this sign test a “distribution-free test”?

September weight (kg)

67

53

64

74

67

70

55

74

62

57

April weight (kg)

66

52

68

77

67

71

60

82

65

58

Short Answer

Expert verified
  • The only requirement for conducting a sign test is that the two samples should be simple random samples.
  • No, there is no requirement for the populations of the given samples to follow a certain distribution, such as normal distribution or any other distribution.
  • As there is no strict requirement for the populations to follow a certain distribution, the sign test can be regarded as the ‘distribution-free test’.

Step by step solution

01

Given information

Two samples are given showing the weights of students (kgs) in September and April.

02

State the assumptions of the sign test

The sign test is a type of non-parametric test that can be used to test the claim of no difference in the values of the two samples.

The following are the only requirements for conducting a sign test.

1. The sample data should be a simple random sample.

2. There is no requirement for the populations of the samples to follow a specific distribution, such as normal distribution or any other distribution.

3. As there is no assumption regarding the distribution of the populations, the sign test can be regarded as a ‘distribution-free test’.

The stated results are satisfied by the three assumptions of the sign test.

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Most popular questions from this chapter

Nonparametric Tests

a. Which of the following terms is sometimes used instead of “nonparametric test”: normality test; abnormality test; distribution-free test; last testament; test of patience?

b. Why is the term that is the answer to part (a) better than “nonparametric test”?

Nominal Data. In Exercises 9–12, use the sign test for the claim involving nominal data.

Medical Malpractice In a study of 1228 randomly selected medical malpractice lawsuits, it was found that 856 of them were dropped or dismissed (based on data from the Physicians Insurers Association of America). Use a 0.01 significance level to test the claim that there is a difference between the rate of medical malpractice lawsuits that go to trial and the rate of such lawsuits that are dropped or dismissed.

Finding Critical Values Assume that we have two treatments (A and B) that produce quantitative results, and we have only two observations for treatment A and two observations for treatment B. We cannot use the Wilcoxon signed ranks test given in this section because both sample sizes do not exceed 10.

Rank

Rank Sum of Treatment A

1

2

3

4


A

A

B

B

3

a. Complete the accompanying table by listing the five rows corresponding to the other five possible outcomes, and enter the corresponding rank sums for treatment A.

b. List the possible values of R and their corresponding probabilities. (Assume that the rows of the table from part (a) are equally likely.)

c. Is it possible, at the 0.10 significance level, to reject the null hypothesis that there is no difference between treatments A and B? Explain.

Using Nonparametric Tests. In Exercises 1–10, use a 0.05 significance level with the indicated test. If no particular test is specified, use the appropriate nonparametric test from this chapter.

California Lottery Listed below are consecutive first-digits drawn in the California Daily 4 lottery. Test for randomness of even and odd integers. Does the lottery appear to be working as it should?

5

2

2

8

4

8

8

7

1

0

6

4

1

5

1

5

5

3

1

4

1

5

0

0

3

9

6

6

3

7

Matched Pairs.In Exercises 5–8, use the sign test for the data consisting of matched pairs.

Speed Dating: Attractiveness Listed below are “attractiveness” ratings (1 = not attractive; 10 = extremely attractive) made by couples participating in a speed dating session. The listed ratings are from Data Set 18 “Speed Dating”. Use a 0.05 significance level to test the claim that there is a difference between female attractiveness ratings and male attractiveness ratings.

Rating of Male by Female

4

8

7

7

6

8

6

4

2

5

9.5

7

Rating of Female by Male

6

8

7

9

5

7

5

4

6

8

6

5
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