Conduct the following test at the a = 0.05 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, #P2. Sample data are x, = 28, n, = 255, x2 = 38, and n2 = 302. (a) Determine the null and alternative hypotheses. Choose the correct answer below. O A. Ho: P, = p2 versus H,: p, P2 O D. Ho: P, = 0 versus H,: p, = 0 (b) The test statistic z, is. (Round to two decimal places as needed.) (c) The P-value is (Round to three decimal places as needed.) Test the null hypothesis. Choose the correct conclusion below. O A. Do not reject the null hypothesis because there is sufficient evidence to conclude that P, >P2. O B. Reject the null hypothesis because there sufficient evidence to conclude that p, P2. OC. Do not reject the null hypothesis because there is not sufficient evidence to conclude that p, #p2- O D. Reject the null hypothesis because there is not sufficient evidence to conclude that p, <2
Conduct the following test at the a = 0.05 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, #P2. Sample data are x, = 28, n, = 255, x2 = 38, and n2 = 302. (a) Determine the null and alternative hypotheses. Choose the correct answer below. O A. Ho: P, = p2 versus H,: p, P2 O D. Ho: P, = 0 versus H,: p, = 0 (b) The test statistic z, is. (Round to two decimal places as needed.) (c) The P-value is (Round to three decimal places as needed.) Test the null hypothesis. Choose the correct conclusion below. O A. Do not reject the null hypothesis because there is sufficient evidence to conclude that P, >P2. O B. Reject the null hypothesis because there sufficient evidence to conclude that p, P2. OC. Do not reject the null hypothesis because there is not sufficient evidence to conclude that p, #p2- O D. Reject the null hypothesis because there is not sufficient evidence to conclude that p, <2
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:## Hypothesis Testing at α = 0.05 Significance Level
**Objective:**
Conduct a hypothesis test to determine whether \( p_1 \neq p_2 \). The sample data are as follows: \( x_1 = 28 \), \( n_1 = 255 \), \( x_2 = 38 \), \( n_2 = 302 \). Assume simple random sampling.
### Steps:
### (a) Determine the Null and Alternative Hypotheses:
Choose the correct pair:
- **A.** \( H_0: p_1 = p_2 \) versus \( H_1: p_1 < p_2 \)
- **B.** \( H_0: p_1 = p_2 \) versus \( H_1: p_1 \neq p_2 \)
- **C.** \( H_0: p_1 = p_2 \) versus \( H_1: p_1 > p_2 \)
- **D.** \( H_0: p_1 = 0 \) versus \( H_1: p_1 = 0 \)
### (b) Test Statistic \( z_0 \):
Calculate and fill in the test statistic value.
- \( z_0 = \_ \) (Round to two decimal places as needed.)
### (c) P-value:
Determine and input the P-value.
- P-value = \_ (Round to three decimal places as needed.)
### Conclusion:
Choose the correct conclusion about the null hypothesis:
- **A.** Do not reject the null hypothesis because there is sufficient evidence to conclude that \( p_1 > p_2 \).
- **B.** Reject the null hypothesis because there is sufficient evidence to conclude that \( p_1 \neq p_2 \).
- **C.** Do not reject the null hypothesis because there is not sufficient evidence to conclude that \( p_1 \neq p_2 \).
- **D.** Reject the null hypothesis because there is not sufficient evidence to conclude that \( p_1 < p_2 \).
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