Question

conduct a 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 the samples were obtained independently from a large population using simple random sampling. test whether $p_1>p_2$. the sample data are $x_1 = 126$, $n_1 = 257$, $x_2 = 135$, and $n_2 = 317$. (b) determine the test statistic. $z_0 = 1.53$ (round to two decimal places as needed.) (c) determine the p - value. the p - value is $0.063$. (round to three decimal places as needed.) what is the result of this hypothesis test? a. do not reject the alternative hypothesis because there is sufficient evidence to conclude that $p_1\
eq p_2$. b. do not reject the null hypothesis because there is not sufficient evidence to conclude that $p_1>p_2$. c. reject the null hypothesis because there is sufficient evidence to conclude that $p_1>p_2$. d. reject the null hypothesis because there is sufficient evidence to conclude that $p_1 < p_2$.

Explanation:

Step1: Compare P - value and significance level

We are given a significance level \(\alpha = 0.10\) and a P - value of \(0.063\).
Since \(P - value=0.063<\alpha = 0.10\)

Step2: Make a decision based on the comparison

When \(P - value<\alpha\), we reject the null hypothesis \(H_0\).
The null hypothesis \(H_0:p_1 = p_2\) and the alternative hypothesis \(H_1:p_1>p_2\) (from the problem statement "Test whether \(p_1 > p_2\)")

Answer:

C. Reject the null hypothesis because there is sufficient evidence to conclude that \(p_1 > p_2\)