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) 31 31 31 32 36 28 29 40 31 35

Actor (years) 60 34 38 40 29 35 51 35 38 40

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, ?_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?

H_o: ?_d = ___ (years)

H_1:?_d < ____ (years)

Identify the test statistic.

t = _____ (Round to two decimal places as? needed.)

Identify the p-value.

p= ____ (Round to three decimal places as needed.)

(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 level is ____ year (s) < ?_d < ____ year (s). Round to one decimal place.

Answer 1

Ho" ?d = 0

H1: ?d < 0

t=-2.21

p value =0.027

b)

for 90% CI; and 9 degree of freedom, value of t=			1.833
therefore confidence interval=		sample mean -/+ t*std error
margin of errror          =t*std error=		6.310
lower confidence limit                     =		-13.910
upper confidence limit                    =		-1.290

The confidence level is -13.9 year (s) < ?d < -1.3 year (s)