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.

Speed Dating In a study of speed dating conducted at Columbia University, female subjects were asked to rate the attractiveness of their male dates, and a sample of the results is listed below (1 = not attractive; 10 = extremely attractive). Use the sign test to test the claim that the sample is from a population with a median equal to 5.

5	8	3	8	6	10	3	7	9	8
5	5	6	8	8	7	3	5	5	6
8	7	8	8	8	7

A sample is given showing the male attractiveness ratings by females.

The sign test is used to test the claim that the sample comes from a population with a median equal to 5.

The null hypothesis is as follows:

The given sample comes from a population with a median equal to 5.

The alternative hypothesis is as follows:

The given sample comes from a population with a median not equal to 5.

If the value of the test statistic is greater than the critical value the null hypothesis is rejected, else it is failed to reject.

The total number of values (n) is equal to 26.

Assign a positive value to all the observations greater than 5 and a negative value to all the observations less than 5.

Discard all those values equal to 5.

The following table shows the signs:

18 positive signs correspond to values greater than 5 and 3 negative signs correspond to values less than 5.

Letx be the number of times the less frequent sign occurs.

Thus, x = 3.

Here, n be the total number of positive and negative signs, which is equal to 21.

Here, \(n \le 25\), so the test statistic is equal to x; that is, the test statistic value is equal to 3.

The critical value at\(\alpha = 0.05\)and n = 21 for a two-tailed test is equal to 5.

Since the test statistic is less than the critical value, the null hypothesis is rejected.

There is enough evidence to warrant rejection of the claim that the sample comes from a population with a median equal to 5.