Question

Consider the hypothesis test below. H. : P1 - P20 H. : P1 P2 > 0 The following results are for independent samples taken from the two populations. Sample 2 Sample 1 11 = 100 ©1 = 0.27 n2 = 300 P2 = 0.18 Use pooled estimator of p. a. What is the value of the test statistic (to 2 decimals)? .16 b. What is the p-value (to 4 decimals)? 1.89 c. With a = .05, what is your hypothesis testing conclusion? Conclude the difference between the proportions is greater than 0 1

Answer 1

Given that Hoip,-P2 oso H:P, -P270 ni-100 nz=300 R2 = 0.18 E = 0.27 pooled estimator of p p = Xit X2 nitna

= nipit na P2 10o (0.27 ) + 300(O.18) loot 300 = = 8 27 +54 400 = 0.2025 IP @ test ar statistic i P2 0. 27 0.18 0.2025 L t oo yoo 6-2025 0.01 +0.00333 8. 2025 Jo.01333 0.2025 (0.11547) = 0.09 0.0234 Ical = 3.85 IP value = P(Z > Zcal) = P(Z >3.85) = 1 - P(Z <3.85) = 1-0.9999 TP-value = o.oooll

Decision 2 t = 0.05 Pralve < = 0.0ool L Ho if p value Regect e Here P va - we reject Ho concesion we may conclude that the difference between the proportions is greater than o -