The following data lists the ages of a random selection of actresses when they won an award in the category of BestActress, 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.

Actress(years)

29

28

28

30

36

24

25

41

28

36

Actor(years)

58

40

35

39

32

31

47

42

39

39

a. Use the sample data with a 0.05 significance level to test the claim that for the population of ages of Best Actresses and BestActors, the differences have a mean less than 0(indicating that the Best Actresses are generally younger than BestActors).

In thisexample, d is the mean value of the differences d for the population of all pairs ofdata, where each individual difference d is defined as theactress's age minus theactor's age. What are the null and alternative hypotheses for the hypothesistest?