Question

The following data set shows the ages of the Best Actress and Best Actor award at a given awards show for various years:

Actress Age	Actor Age
24	44
36	36
24	40
37	54
22	50
37	53
24	44
27	43
32	65
36	44
32	57

Using a Sign Test, test the claim that there is no median difference between the ages of Best Actress and Best Actor award winners.

Find the null and alternative hypothesis.

H0: A)The median of the differences is NOT zero. B)The median of the differences is zero. C)The median age of actresses is more than the median age of actors. D)The median age of actresses is less than the median age of actors.

H1: A)The median age of actresses is less than the median age of actors. B)The median of the differences is zero. C)The median of the differences is NOT zero. D)The median age of actresses is more than the median age of actors.

If we consider + to represent when the female was older than the male, then how many of each sign is there?

Positive Signs:

Negative Signs:

Total Signs:

What is the p-value?

At a 0.025 significance, what is the conclusion about the null? A)Support the null hypothesis. B)Reject the null hypothesis. C)Fail to reject the null hypothesis. D)Fail to support the null hypothesis.

What is the conclusion about the claim? A)Support the claim that there is no mean difference in the ages. B)There is insufficient evidence to support the claim that there is no mean difference in the ages. C)Reject the claim that there is no mean difference in the ages. D)Fail to reject the claim that there is no mean difference in the ages.

Let's now perform a mean-matched pairs test to test the claim that there is no mean difference between the age of males and females. For the context of this problem, d=x2−x1d=x2-x1 where the first data set represents actress (female) ages and the second data set represents male (actor) ages. We'll continue to use a significance of 0.025. You believe the population of difference scores is normally distributed, but you do not know the standard deviation.

H0: μd=0

H1:μd≠0

Actress Age	Actor Age
24	44
36	36
24	40
37	54
22	50
37	53
24	44
27	43
32	65
36	44
32	57

What is the critical value for this test? t=±

What is the test statistic for this sample? t=

What is the p-value? (Round to three decimal places.)

Conclusion about the null: A)Support the null hypothesis. B)Reject the null hypothesis. C)Fail to reject the null hypothesis. D)Fail to support the null hypothesis.

Conclusion about the claim: A)Support the claim that there is no mean difference in the ages. B)There is insufficient evidence to support the claim that there is no mean difference in the ages. C)Reject the claim that there is no mean difference in the ages. D)Fail to reject the claim that there is no mean difference in the ages.

How were these two tests similar?

How were these two tests different?

Answer 1

Part I

X	Y	D=X-Y	Mod D	Rank= Mod(D)
24	44	-20	20	6.5
36	36	0	0
24	40	-16	16	3
37	54	-17	17	5
22	50	-28	28	9
37	53	-16	16	3
24	44	-20	20	6.5
27	43	-16	16	3
32	65	-33	33	10
36	44	-8	8	1
32	57	-25	25	8

Part II

X	Y	X square	Y square
24	44	576	1936
36	36	1296	1296
24	40	576	1600
37	54	1369	2916
22	50	484	2500
37	53	1369	2809
24	44	576	1936
27	43	729	1849
32	65	1024	4225
36	44	1296	1936
32	57	1024	3249
331	530	10319	26252
X bar	30.09091
Y bar	48.18182
X bar- Y bar	-18.0909
S1=	11.24443		S1 square	126.4372
S2=	17.42735		S2 square	303.7124
S=	15.45872

Both tests reject H0 and conclude that actress age and actors age are having different mean and median.