Question

0.10. You wish to test the following claim (Ha) at a significance level of a = H:pi = P2 Ha:pi + P2 You obtain 382 successes in a sample of size 779 from the first population. You obtain 139 successes in a sample of size 250 from the second population. What is the test statistic for this sample? (Report answer accurate to three decimal places.) Test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... O less than (or equal to) a Ogreater than a This test statistic leads to a decision to... Oreject the null O accept the null O fail to reject the null

Answer 1

Sol > Given data, Xi = 382 ↑ The first population ni = 779 X2 = 139 7 The second population N2 = 250 Significance level (x)=0.10 Ho :P, = P2 Ha ! P, # Pz (Two tailed test) 382 then, ệ, a = 0.4904 X ni 11 779 X2 139 0.556 Nos ol N₂ 250 the value of hooled proportion, 382 + 139 Ni+Xz pa nit na 779 +250 521 1029 p = 0.50 13

test statistic cz), år 2 Z = (1-P) * ( tha) 0.4904 0.556 0.5063 * 0.4937 * 1+1 779 250 -0.0656 0.0364 N 1.8027 P-value = (2-0:10, 2=-1.802) P-value = 10.0715 -> reject (Ho) 0 P-value is less them com equal to significamcelevel.com Coption (I) is correct) This test statistic leads to a decision to reject the null hypothesia. [option (I) is correct