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

Speed Dating: Attributes Listed below are “attribute” ratings made by couples participating in a speed dating session. Each attribute rating is the sum of the ratings of five attributes (sincerity, intelligence, fun, ambition, shared interests). The listed ratings are from Data Set 18 “Speed Dating” in Appendix B. Use a 0.05 significance level to test the claim that there is a difference between female attribute ratings and male attribute ratings.

Rating of Male by Female	29	38	36	37	30	34	35	23	43
Rating of Female by Male	36	34	34	33	31	17	31	30	42

The two samples of data are given as the ratings of males and females.

The sign test is the non-parametric test used to test the difference between male and female attribute ratings.

The null hypothesis is as follows:

There is no difference between male and female attribute ratings.

The alternative hypothesis is as follows:

There is a difference between male and female attribute ratings.

The test is two-tailed.

If the male rating value is greater than the female rating, the sign of difference is positive.

If the male rating value is less than the female rating, the sign of difference is negative.

If the value of the Male rating is equal to the Female rating, the difference is zero.

The sign of the difference table is as follows:

The number of positive signs is equal to 6.

The number of negative signs is equal to 3.

The sample size (n) is equal to 9.

Upon observing the number of positive and negative signs, there seems to be a difference in the occurrence of signs, and thus, the observation does not contradict the alternative hypothesis.

Since n is less than 25, the test statistic value (x) is the number of times the less frequent sign occurs.

The less frequent sign is the negative sign, and it occurs three times.

Thus, x= 3.

Referring to Table A-7, the critical value of x for n = 9 and\(\alpha \)=0.05 for a two-tailed test equals 1.

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

If the test statistic value is less than or equal to the critical value, the null hypothesis is rejected.

As the calculated value of x equal to 3 is greater than the critical value of 1, the null hypothesis is failed to reject.

There is not enough evidence to conclude that there is a difference in the female attribute ratings and the male attribute ratings.