Question

The following data lists the ages of a random selection of actresses when they won an award in the category of Best​ Actress, along with the ages of actors when they won in the category of Best Actor. The ages are matched according to the year that the awards were presented. Complete parts​ (a) and​ (b) below.

Use the sample data with a

0.050.05

significance level to test the claim that for the population of ages of Best Actresses and Best​ Actors, the differences have a mean less than 0​ (indicating that the Best Actresses are generally younger than Best​Actors).

In this​ example, md 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?

Actress (years)   Actor (years)
28   56
27   41
31   34
26   37
39   36
24   31
24   54
38   35
33   34
36   42

Answer 1

where

test statistic,t=Md/Sd/sqrt(n)

=(-9.4)/(11.69235268/sqrt(10))

t=-2.542295

df=n-1=10-1=9

P value in excel

=T.DIST(-2.542295,9,TRUE)

=0.0157958

p<0.05

Reject Ho

Accept Ha

There is sufficient statistical evidence at 5% level of significance to conclude that he mean value of the differences d for the population of all pairs of​ data,