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   28 34 32 33 26 23 39 31 37 Actor (years) 57   41   38 34 27 32 56 40 36 44   a. 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 = __ ​year(s) H1​: μd < __  ​year(s) ​(Type integers or decimals. Do not​ round.)   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 _________ the significance​ level, ________ the null hypothesis. There ____ sufficient evidence to support the claim that actresses are generally younger when they won the award than actors.   b. Construct the confidence interval that could be used for the hypothesis test described in part​ (a). What feature of the confidence interval leads to the same conclusion reached in part​ (a)?   The confidence interval is ___ ​year(s) < μd < 2.4 ​year(s). ​(Round to one decimal place as​ needed.)   What feature of the confidence interval leads to the same conclusion reached in part​ (a)?    Since the confidence interval contains ____   _______ the null hypothesis

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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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

 

28

34

32

33

26

23

39

31

37

Actor (years)

57

 

41

 

38

34

27

32

56

40

36

44

 

a. 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 = __ ​year(s)

H1​: μd < __  ​year(s)

​(Type integers or decimals. Do not​ round.)

 

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 _________ the significance​ level, ________ the null hypothesis. There ____ sufficient evidence to support the claim that actresses are generally younger when they won the award than actors.

 

b. Construct the confidence interval that could be used for the hypothesis test described in part​ (a). What feature of the confidence interval leads to the same conclusion reached in part​ (a)?

 

The confidence interval is ___ ​year(s) < μd < 2.4 ​year(s).

​(Round to one decimal place as​ needed.)

 

What feature of the confidence interval leads to the same conclusion reached in part​ (a)? 

 

Since the confidence interval contains ____   _______ the null hypothesis.

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