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
31	62
22	42
33	55
37	57
24	30
33	49
23	54
29	50
24	53
27	37
23	35
32	40
25	63
23	44
28	39

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: ______________

H1: _________________

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? ____________ (Round to three decimal places.)

At a 0.025 significance, what is the conclusion about the null? __________________

2. What is the conclusion about the claim? _______________________

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−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
31	62
22	42
33	55
37	57
24	30
33	49
23	54
29	50
24	53
27	37
23	35
32	40
25	63
23	44
28	39

What is the critical value for this test? t=± ____________ (Round to three decimal places.)

What is the test statistic for this sample? t= ____________ (Round to three decimal places.)

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

Conclusion about the null: ______________

Conclusion about the claim: _________________

How were these two tests similar? __________________________

How were these two tests different? _______________________

Answer 1

1. H0:  there is no median difference between the ages of Best Actress and Best Actor award winners.

H1:  there is median difference between the ages of Best Actress and Best Actor award winners.

Let the los be alpha = 0.025

From the given data

S.No.	Actress Age	Actor Age	Diff = X-Y
1	31	62	-31
2	22	42	-20
3	33	55	-22
4	37	57	-20
5	24	30	-6
6	33	49	-16
7	23	54	-31
8	29	50	-21
9	24	53	-29
10	27	37	-10
11	23	35	-12
12	32	40	-8
13	25	63	-38
14	23	44	-21
15	28	39	-11

Calim: Thus we conclude that  there is median difference between the ages of Best Actress and Best Actor award winners.

2) Paired t test

H0:  there is no median difference between the ages of Best Actress and Best Actor award winners.

H1:  there is median difference between the ages of Best Actress and Best Actor award winners.

Let the los be alpha = 0.025

From the given data

S.No.	Actress Age	Actor Age	Difference (d)	d^2
1	31	62	31.00	961.00
2	22	42	20.00	400.00
3	33	55	22.00	484.00
4	37	57	20.00	400.00
5	24	30	6.00	36.00
6	33	49	16.00	256.00
7	23	54	31.00	961.00
8	29	50	21.00	441.00
9	24	53	29.00	841.00
10	27	37	10.00	100.00
11	23	35	12.00	144.00
12	32	40	8.00	64.00
13	25	63	38.00	1444.00
14	23	44	21.00	441.00
15	28	39	11.00	121.00
	Total :	296.00	7094.00

Test Statistic, t: 8.0788

Critical t: ±2.5096

P-Value: 0.0000

since t value is not in t critical values and P-value < alpha = 0.05 so we reject H0

Thus we conclude that there is median difference between the ages of Best Actress and Best Actor award winners.