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. Actress left parenthesis years right parenthesis 29 31 32 31 33 26 24 44 31 35 Actor left parenthesis years right parenthesis 62 41 32 38 30 36 50 40 41 42

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 Best​ Actors, the differences have a mean less than 0​ (indicating that the Best Actresses are generally younger than Best​ Actors). In this​ example, mu Subscript d 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?

Upper H 0​: mu Subscript d ▼ nothing ​year(s) Upper H 1​: mu Subscript d ▼ not equals greater than equals less than nothing ​year(s) ​(Type integers or decimals. Do not​ round.)

Identify the test statistic. tequals nothing ​(Round to two decimal places as​ needed.)

Identify the​ P-value. ​P-valueequals nothing ​(Round to three decimal places as​ needed.)

What is the conclusion based on the hypothesis​ test? Since the​ P-value is ▼ greater than less than or equal to the significance​ level, ▼ fail to reject reject the null hypothesis. There ▼ is is not sufficient evidence to support the claim that actresses are generally younger when they won the award than actors.

Answer 1

(i)

H0: 0

H1: 0

(ii)

Values for d are got as follows:

- 33, - 10, 0, - 7, 3, - 10, -26, 4, - 10, - 7

From the d values, the following statistics are calculated:

n = 10

= - 96/10 = - 9.6

s_d = 11.8622

SE = s_d/

= 11.8622/ = 3.7512

Test statistic is:

t = - 9.6/3.7512 = - 2.56

So,

The test statistic is:

t = - 2.56

(iii)

ndf = n - 1 = 10 - 1 = 9

By Technology, p - value= 0.015

So,

p - value = 0.015

(iv)

Since the P - value is less than the significance level, reject the null hypothesis. There is sufficient evidence to support the claim that actresses are generally younger when they won the award than actors.