Conduct a test at the a = 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 ra sampling. Test whether p, >P2. The sample data are x, = 120, n, = 249, x2 = 137, and n, = 312. (a) Choose the correct null and alternative hypotheses below. O A. Ho: P,P2 versus H,: p, #P2 O B. Ho: P, = P2 versus H: p, P2 O D. Ho: P, = 0 versus H,: P. *0 (b) Determine the test statistic. Z= (Round to two decimal places as needed.) (c) Determine the P-value. The P-value is (Round to three decimal places as needed.) What is the result of this hypothesis test? O A. Reject the null hypothesis because there is sufficient evidence to conclude that p,

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Conduct a test at the \(\alpha = 0.01\) 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 \(p_1 > p_2\). The sample data are \(x_1 = 120\), \(n_1 = 249\), \(x_2 = 137\), and \(n_2 = 312\).

(a) Choose the correct null and alternative hypotheses below.

- A. \(H_0: p_1 = p_2\) versus \(H_1: p_1 \neq p_2\)
- B. \(H_0: p_1 = p_2\) versus \(H_1: p_1 < p_2\)
- C. \(H_0: p_1 = p_2\) versus \(H_1: p_1 > p_2\)
- D. \(H_0: p = 0\) versus \(H_1: p \neq 0\)

(b) Determine the test statistic.

\(z_0 = \square\) (Round to two decimal places as needed.)

(c) Determine the P-value.

The P-value is \(\square\). (Round to three decimal places as needed.)

What is the result of this hypothesis test?

- A. Reject the null hypothesis because there is sufficient evidence to conclude that \(p_1 < p_2\).
- B. Do not reject the null hypothesis because there is not sufficient evidence to conclude that \(p_1 > p_2\).
- C. Do not reject the null hypothesis because there is not sufficient evidence to conclude that \(p_1 \neq p_2\).
- D. Do not reject the null hypothesis because there is not sufficient evidence to conclude that \(p_1 \neq p_2\).
Transcribed Image Text:Conduct a test at the \(\alpha = 0.01\) 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 \(p_1 > p_2\). The sample data are \(x_1 = 120\), \(n_1 = 249\), \(x_2 = 137\), and \(n_2 = 312\). (a) Choose the correct null and alternative hypotheses below. - A. \(H_0: p_1 = p_2\) versus \(H_1: p_1 \neq p_2\) - B. \(H_0: p_1 = p_2\) versus \(H_1: p_1 < p_2\) - C. \(H_0: p_1 = p_2\) versus \(H_1: p_1 > p_2\) - D. \(H_0: p = 0\) versus \(H_1: p \neq 0\) (b) Determine the test statistic. \(z_0 = \square\) (Round to two decimal places as needed.) (c) Determine the P-value. The P-value is \(\square\). (Round to three decimal places as needed.) What is the result of this hypothesis test? - A. Reject the null hypothesis because there is sufficient evidence to conclude that \(p_1 < p_2\). - B. Do not reject the null hypothesis because there is not sufficient evidence to conclude that \(p_1 > p_2\). - C. Do not reject the null hypothesis because there is not sufficient evidence to conclude that \(p_1 \neq p_2\). - D. Do not reject the null hypothesis because there is not sufficient evidence to conclude that \(p_1 \neq p_2\).
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