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 (years)	30	26	28	26	37	27	25	42	31	35
Actor (years)	62	34	33	38	27	33	54	41	34	44

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, 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=   

​(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, (reject/fail to 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

frm above:

null Hypothesis:μd	=	0
alternate Hypothesis: μd	<	0

test statsitic t =-2.31

p value =0.023

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