Question

Conduct a test at the alpha α equals = 0.01 0.01 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 p 1 greater than p 2 p1>p2. The sample data are x 1 equals 119 x1=119​, n 1 equals 249 n1=249​, x 2 equals 135 x2=135​, and n 2 equals 305 n2=305. Thank you for your help.

Answer 1

= 119/249 = 0.48

= 135/305 = 0.44

The pooled proportion (P) = ( * n1 + * n2)/(n1 + n2)

= (0.48 * 249 + 0.44 * 305)/(249 + 305) = 0.46

SE = sqrt(P(1 - P)(1/n1 + 1/n2))

= sqrt(0.46 * (1 - 0.46) * (1/249 + 1/305))

= 0.043

The test statistic z = ()/SE

= (0.48 - 0.44)/0.043 = 0.93

P-value = P(Z > 0.93)

= 1 - P(Z < 0.93)

= 1 - 0.8238 = 0.1762

Since the p-value is greater than the significance level (0.1762 > 0.01), so we should not reject the null hypothesis.