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.

Use a 0.01 significance level

1. H0: μd = 0 years

H1: μd< 0 years

Actress (years)	28	31	28	27	33	26	24	40	33	36
Actor (years)	65	41	34	42	27	33	55	39	33	41

Use 0.01 significance level 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

Answer 1

Step 1 : Find the mean and standard deviation for the difference in the age as shown below.

Step 2 : Find 99% confidence interval.

The 99% confidence interval for the difference is (-24.6087, 3.8087).

Since the confidence interval contains zero, it is not statistically significant.

Hence we can say that at a significance level of 0.01, the difference between the age of the actress and actors is not significantly different from zero.