Conduct the following test at the \( \alpha = 0.10 \) 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 \( p_1 \ne p_2 \). Sample data are \( x_1 = 30 \), \( n_1 = 255 \), \( x_2 = 36 \), and \( n_2 = 301 \).
(a) Determine the null and alternative hypotheses. Choose the correct answer below.
OA. \( H_0: p_1 = p_2 \) versus \( H_1: p_1 > p_2 \)
OC. \( H_0: p_1 = p_2 \) versus \( H_1: p_1 \ne p_2 \)
(b) The test statistic \( z_0 \) is . (Round to two decimal places as needed.)
OB. \( H_0: p_1 = 0 \) versus \( H_1: p_1 = 0 \)
OD. \( H_0: p_1 = p_2 \) versus \( H_1: p_1 < p_2 \)