Question

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

• 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

Given information

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

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.