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) 25 Actor (years) 59 31 28 29 36 26 27 39 37 40 36 31 33 51 36 32 35 34 39 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, Hd 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 H: Pd year(s) year(s) (Type integers or decimals. Do not round.) Several students were tested for reaction times (in thousandths of a second) using their right and left hands. (Each value is the elapsed time between the release of a strip of paper and the instant that it is caught by the subject.) Results from five of the students are included in the graph to the right. Use a 0.02 significance level to test the claim that there is no difference between the reaction times of the right and left hands. Click the icon to view the reaction time data table. Left Hand 200- What are the hypotheses for this test? Let Hd be the Ho Hd 0 H Hd 0 mean of the differences difference between the means Reaction Time Data Table of the right and left hand reaction times. Right Hand Left Hand 128 146 117 152 143 171 170 182 161 189 Print Done O 170- 140 100 140 180 Right Hand A popular theory is that presidential candidates have an advantage if they are taller than their main opponents. Listed are heights (in centimeters) of randomly selected presidents along with the heights of their main opponents. Complete parts (a) and (b) below. Height (cm) of President 188 187 171 191 187 177 Height (cm) of Main Opponent 182 183 172 183 196 181 a. Use the sample data with a 0.01 significance level to test the claim that for the population of heights for presidents and their main opponents, the differences have a mean greater than 0 cm. 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 president's height minus their main opponent's height. What are the null and alternative hypotheses for the hypothesis test? Ho: Ha H: Hd cm cm (Type integers or decimals. Do not round.)