To test Ho: p=0.50 versus H₁: p>0.50, a simple random sample of n = 200 individuals is obtained and x = 69 successes are observed. (a) What does it mean to make a Type II error for this test? (b) If the researcher decides to test this hypothesis at the x = 0.01 level of significance, compute the probability of making a Type II error, ß, if the true population proportion is 0.54. What is the power of the test? (c) Redo part (b) if the true population proportion is 0.56. (a) What does it mean to make a Type II error for this test? Choose the correct answer below. O A. Ho is not rejected and the true population proportion is greater than 0.50. OB. Ho is not rejected and the true population proportion is equal to 0.50. OC. Ho is rejected and the true population proportion is less than 0.50. O D. Ho is rejected and the true population proportion is greater than 0.50. (b) If the researcher decides to test this hypothesis at the x = 0.01 level of significance, compute the probability of making a Type II error, B, if the true population proportion is 0.54. What is the power of the test? B = Power = (Type integers or decimals rounded to four decimal places as needed.) (c) Redo part (b) if the true population proportion is 0.56. B = Power = (Type integers or decimals rounded to four decimal places as needed.)
To test Ho: p=0.50 versus H₁: p>0.50, a simple random sample of n = 200 individuals is obtained and x = 69 successes are observed. (a) What does it mean to make a Type II error for this test? (b) If the researcher decides to test this hypothesis at the x = 0.01 level of significance, compute the probability of making a Type II error, ß, if the true population proportion is 0.54. What is the power of the test? (c) Redo part (b) if the true population proportion is 0.56. (a) What does it mean to make a Type II error for this test? Choose the correct answer below. O A. Ho is not rejected and the true population proportion is greater than 0.50. OB. Ho is not rejected and the true population proportion is equal to 0.50. OC. Ho is rejected and the true population proportion is less than 0.50. O D. Ho is rejected and the true population proportion is greater than 0.50. (b) If the researcher decides to test this hypothesis at the x = 0.01 level of significance, compute the probability of making a Type II error, B, if the true population proportion is 0.54. What is the power of the test? B = Power = (Type integers or decimals rounded to four decimal places as needed.) (c) Redo part (b) if the true population proportion is 0.56. B = Power = (Type integers or decimals rounded to four decimal places as needed.)
MATLAB: An Introduction with Applications
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Chapter1: Starting With Matlab
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Transcribed Image Text:**Hypothesis Testing: Example Problem and Solution**
To test \( H_0: p = 0.50 \) versus \( H_1: p > 0.50 \), a simple random sample of \( n = 200 \) individuals is obtained, and \( x = 69 \) successes are observed.
### Questions:
**(a) What does it mean to make a Type II error for this test?**
**(b) If the researcher decides to test this hypothesis at the \( \alpha = 0.01 \) level of significance, compute the probability of making a Type II error, \( \beta \), if the true population proportion is 0.54. What is the power of the test?**
**(c) Redo part (b) if the true population proportion is 0.56.**
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### Answers:
**(a) What does it mean to make a Type II error for this test? Choose the correct answer below.**
- \( H_0 \) is not rejected and the true population proportion is greater than 0.50.
- \( H_0 \) is not rejected and the true population proportion is equal to 0.50.
- \( H_0 \) is rejected and the true population proportion is less than 0.50.
- \( H_0 \) is rejected and the true population proportion is greater than 0.50.
**(b) If the researcher decides to test this hypothesis at the \( \alpha = 0.01 \) level of significance, compute the probability of making a Type II error, \( \beta \), if the true population proportion is 0.54. What is the power of the test?**
- \( \beta = \) \_\_\_\_\_
- **Power =** \_\_\_\_\_
- *(Type integers or decimals rounded to four decimal places as needed.)*
**(c) Redo part (b) if the true population proportion is 0.56.**
- \( \beta = \) \_\_\_\_\_
- **Power =** \_\_\_\_\_
- *(Type integers or decimals rounded to four decimal places as needed.)*
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### Diagrams and Calculation Explanations:
There are no diagrams or graphs presented in this text. If calculations were required, they would follow standard procedures for hypothesis testing and power analysis.
**Calculations for
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