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 29 28 27 34 24 23 38 33 36 Actor (years) 63 40 37 40 32 33 51 43 37 41 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, uq 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? Ho: Hd year(s) H1: Hd 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-value = (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 interval is year(S) 0 . H _0 4 983 6.25 19 1361 5.95 1 d 1- Ha , 5 1136 i025 20 7 98 6.09 6 6.16 5.88 ldentify the test statistic 7' 6.33 3.36 g; 1: 3E1) 2;: 0 0.44 8.40 i t: (Round to two deoirnal places as needed.) 9 g 55 9.20 :3 1:3: 3:113 _ 10 7.57 5.92 ' ldentify the Pivalue 11 6 96 7.60 i: 12):: E2; 12 16.08 14.36 ' P-value : (Round to three deCimal places as needed) 13 12 43 3757 g; 1333 g: 14 17 65 11.26 ' ' What is the conclusion based on the hypothesis test? 15 g 72 9720 :3 1:3: 13