Question

Conduct a test at the a=0.05 level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the P-value. Assume the samples were obtained independently from a large population using simple random sampling. Test whether pa > P2. The sample data are x = 120, n, 251, x2 = 132 and n, -311 (a) Choose the correct null and alternative hypotheses below O A. Ho P1 =Pz versus H, PP2 OB. Ho P, = P2 versus H, PP2 O C. Ho P40 versus H, P+0 OD. Ho P1 P2 versus Hy P, P2 (b) Determine the test statistic 20- (Round to two decimal places as needed.) (c) Determine the P-value The P-value is (Round to three decimal places as needed) Click to select your answer(s)

Answer 1

Hospi=p2 vis His pixp2 Test statister ~ N(0,1) = Z PI-PL ✓ PCI-PY + + where Pis . pooled proportion => p = nipitmap nitna = x + X₂ nitha = P = 120 + 132 257 +31 = 0.448 = 2 = x XI - X2 ni nz - x2 0.448 (1-0.448 / 1+1 =) Z= 120 - 132 251 311 r 0.247 ( 4 + 2 ) =) Zo= 1.272 Ans. b.) ze = 1.27 | Tobuleted value of 2 = 7o.or= 1.645 (using Mecmeliables) linse Zo <Zresuested. - we feil to reject to at d = 0.05 level of significance Ans. B. Do not reject the nullhypothesis because there is not sufficient evidence widence to conclude to conclude that pip2 that