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.   Actress (years) 28 29 33 32 39 23 23 41 30 32   Actor (years) 66 40 39 42 33 33 51 37 36 40     Use the sample data with a 0.01 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, 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?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
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Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 13PPS
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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.

 

Actress (years)

28

29

33

32

39

23

23

41

30

32

 

Actor (years)

66

40

39

42

33

33

51

37

36

40

 

 

Use the sample data with a 0.01 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, 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?

 

H0​: μd (Choose one of the following:)

               greater than>, less than<, not equals≠, equals=

______​year(s) (Type integers or decimals. Do not​ round.)

 

H1​: μd  (Choose one of the following:)

     greater than>, less than<, equals=, not equals≠

______​year(s)​ (Type integers or decimals. Do not​ round.)

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