Question

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

0.01

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's age	17	26	24	51	30
​Actor's age	40	40	65	55	42

In this​ example,

μd

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=nothing

​(Round to two decimal places as​ needed.)

Identify the​ P-value.

​P-value=nothing

​(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

Actress's age : Actor's age 26 51 30 40 65 SS -12 18-8 798.8 Claim There is difference (Actress's age) - (Actor's Age) 40 42 d : &d=-94 ad 2566 (mean) az ed = 2941 Joti,kad?- (434) = S(2566 —C-Qy2) (standard deviation) Sd = J = [14.1315] between the ages of actresses and actor (Md 70) 2=0.01 signiticance level. Null and altenative hypotheses. Ho: Md=0 Versus Hi: Md to (1) The test statistic (d- Md) =(-18.8-0) 14.1315 (111) afan-1=4 ; The p-value (0.041 Since The P-value Significance level greater than Decision: Ifail to reject) the null hy po thesis There is not subtinent evidence to support the claim That there is difference between the ages of actress and actors. option A 2.97 the