Question

3. Listed below are ages of actresses and actors at the time that they won an award for the categories of Best Actress and Best Actor. Use the sample data to test for a difference between the ages of actresses and actors when they win the award. Use a 0.05 significance level. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal.

Actress_age       Actor_age

16           47

32           46

29           63

59           50

27           44

In this​ example, mu Subscript d is the mean value of the differences d for the population of all pairs of​ data, where each individual difference d is defined as the​ actress's age minus the​ actor's age. What are the null and alternative hypotheses for the hypothesis​ test?

a.H0: µd=0

H1: µd<0

b. H0: µd≠0

H1: µd>0

c. H0: µd≠0

H1: µd=0

d. H0: µd=0

H1: µd≠0

Identify the test statistic.

T=_____

(Round to two decimal places as​ needed.)

Identify the​ P-value.

​P-value=____

(Round to three decimal places as​ needed.)

What is the conclusion based on the hypothesis​ test?

Since the​ P-value is (greater,less) than the significance​ level, (fail to reject/reject)

the null hypothesis. There (is/is not) sufficient evidence to support the claim that there is a difference between the ages of actresses and actors when they win the award.

Answer 1

Ans:

	Actress	Actor	d
1	16	47	-31
2	32	46	-14
3	29	63	-34
4	59	50	9
5	27	44	-17
		d-bar	-17.4
		sd	17.097

Test statistic:

t=(-17.4-0)/(17.097/SQRT(5))

t=-2.28

df=5-1=4

p-value=tdist(2.28,4,2)=0.085

Since the​ P-value is greater,than the significance​ level,fail to reject the null hypothesis. There is not sufficient evidence to support the claim that there is a difference between the ages of actresses and actors when they win the award.