Question

Conduct the following test at the alphaequals0.10 level of significance by determining​ (a) the null and alternative​ hypotheses, (b) the test​ statistic, and​ (c) the critical 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 28​, n 1 equals 255​, x 2 equals 38 and n 2 equals 302.

Answer 1

Given that,

x1 = 28, n1 = 255 and x2 = 38, n2 = 302

sample proportion 1 = 28/255 = 0.1098

sample proportion 2 = 38/302 = 0.1258

a) The null and alternative hypotheses are,

b) pooled proportion is,

Test statistic is,

Test statistic = Z = -0.58

c) critical values at 0.10 level of significance are,

Z^* = ± 1.645

Since, test statistic = -0.58 > -1.645

we fail to reject the null hypothesis (H_{​​​​​​0}​​​​​).