Question

mpare the time spent in the college''s Success Center vervus final reconded in the table below. 17 imate the mcan weekly carnings Anf the lgtjon 0. A 68 91 8. A popular theory is that presidential candidates have an advantage if they are taller than their main opponents. Listed are heiehts (in centimetery) of e with the heights of their main opponents. random sample of presidents alog Height of president (cm) Height of main opponent (cm) 185 173 178 183 175 193 171 173 180 188 178 175 We want to test, at a 0.05 significance level, the claim that for the population of heights of presidents and their main opponents, the differences have a mean greater than 0 cm. (a) (8 pts) State any definition necessary and write the null and alternative hypotheses. State and verify that the requirements are met. (b) (3 pts) Suppose the applicable hypothesis test results in a p-value of 0.1246. Write the conclusion (in context).

Answer 1

Answer:

From the given data, Sample 1 Sample 2 Difference = Sample 1 - Sample 2 185 171 178 180 175 173 183 175 193 188 173 178 Average 181.167 177.5 3.667 St. Dev. 7.387 6.091 6.89 n

From the sample data, it is found that the corresponding sample means are: X1 = 181.167 X2 = 177.5 Also, the provided sample standard deviations are: $i = 7.387 S2 = 6.091 and the sample size is n = 6. For the score differences we have D = 3.667 sp = 6.89

1. Holla=0 Hai Maho a = 0.05 Test- Statistic - Svo 3.667 = 1.304 6.89%86- t = 1.304 p-value = P(t>1.304) = 0.1246 (using table) b) p-value = 0.12 46 > 0.05 since, p-value > significance level, We accept Ho. so, we have not Jufficient evidence to claim that the difference of means is greater than O.