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 31 30 31 28 33 23 24 38 33 32 Actor left parenthesis years right parenthesis 67 40 37 36 31 34 55 39 39 40 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, 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 ▼ greater than equals not equals less than nothing ​year(s) Upper H 1 ​: mu Subscript d ▼ greater than less than not equals equals 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. 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 nothing ​year(s)less than mu Subscript dless thannothing ​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 ▼ only negative numbers, zero, only positive numbers, ▼ reject fail to reject the null hypothesis.

Answer 1

from above test statistic t =-2.96

p value =0.008

Since the​ P-value is less than or equal to 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

The confidence interval is -22.5 < μd <-0.5

Since the confidence interval contains only negative numbers reject the null hypothesis.