Question

Conduct the following test at the alphaequals0.01 level of significance by determining ​(a) the null and alternative​ hypotheses, ​(b) the test​ statistic, and​ (c) the​ P-value. Assume that the samples were obtained independently using simple random sampling. Test whether p 1 not equals p 2. Sample data are x 1 equals 30​, n 1 equals 254​, x 2 equals 38​, and n 2 equals 302.

Answer 1

Given that,

For sample 1 : x1 = 30, n1 = 254 and

For sample 2 : x2 = 38, n2 = 302 and

Pooled proportion is,

a)The null and alternative hypotheses are,

H0 : p1 = p2

Ha : p1 ≠ p2

b)Test statistic is,

=> Test statistic = Z = -0.28

c) p-value = 2 * P(Z < -0.28) = 2 * 0.3897 = 0.7794

=> p-value = 0.7794