Question

Consider the following competing hypotheses and accompanying sample data. Ho: Pi-P2 = 0.20 HA P - P2 = 0.20 X2 = 130 X1 = 150 n = 250 m2 = 400 a. Calculate the value of the test statistic. b. Calculate the p-value. c. At the 5% significance level, what is the conclusion to the test? Can you conclude that the difference between the population proportions differs from 0.20? d. Repeat the analysis with the critical value approach.

Answer 1

solution » Given data, 2 = 150 no = 250 x2 = 130, n2 = 400 150 Los 30.6 2 So im 212 130 400 0.325 PR n2 Ho! P.-P2 = 0.20 HA! Pi-P2 &0.20 Test statistics y Z= (P - P2) - (P, -P2) V PCI-P) + na where, 150t 130 30.6222 PE x +42 nitha 250 + 400 2 - (0.6 - 0.325) – 0.20 1 062222 (1-04220) Jest too) Z 21.9187 za 1.919 6 p-value P- value = = 2* P(Z > 1.919) = 24 0.0275 p-value = 0.055

© x=0.05 (P-value >x=0.05 5) so fail to reject Null Hypothesis. can not conclude that the difference between Population proportion differs from 0.20. the Critical value x=005 Z critical = 1.96 so (z < Zonitical) fail to reject Null Hypothesis. can not conclude that the difference between population proportion differs from 0.20 toe ع لرا