Question

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 176 170 176 190 193 170 Height (cm) of Main Opponent 165 179 171 166 191 185 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, He 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? Hold = 0 cm H:Hd > 0 cm (Type integers or decimals. Do not round.) Identify the test statistic.

Find the test statistic t, p-value and confidence interval for confidence level 90% and 99%.

Answer 1

S.NO A B d=A-B 1 165 179 2 3 171 (d-d BAR)^2 11 64 -9 144 5 4 24 441 2 1 - 15 324 18 978 4 176 170 176 190 193 170 SUM MEAN 5 166 191 185 6 ائلها

Given lato - dfan-) = 6-1=5 a = 3 {(d-d)² = 978 ago a) 2=0.01 978 6-( 13.98571 Hou eld Hi s lld ocm. allo odlin 3 5.7096 0.5254 13.9857 ta = 0.525 1 P-vake T. DISTIRT(0.525,5) P[ty > 0.525] from Exce= - 0.3110 P-valie -0.3110 al-0.9 90% CI 0.9 kutela, df - to05,5 90%CI 2.015 from t tabe) d. I te tood vn 3† 2015x 13.9857) > 3 11.505 90%.CI = -8,505 ; 14.505 29% CI ; 0.99 d=1-0.99 0.01 to stolzde t0.005.5 99%CI I t text 4.032 (from t table) 3+ 4.032x13-98571 VG 3 2 23.021 -20.021 ; 26.021 - 999.CI '= -20-02! ; 26-021