You hear a claim that one fifth of all major-league baseball players were born outside the United States. You take a sample of 75 baseball players and find that 24 of them were born outside the United States. Conduct a hypothesis test to see if your data shows a significant difference from one fifth. Use a significance level of 0.05. a. What should the alternative hypothesis look like? ⒸHA: P > 0.2 ⒸHA: P < 0.2 ⒸHA: P = 0.2 b. Calculate the value of the point estimate. c. Does this meet the success-failure condition? No, we don't have 10 successes and/or we don't have 10 failures Yes, we have at least 10 successes and at least 10 failures. d. Compute the standard error. e. Compute the test statistic. f. What conclusion should we draw regarding H₂? O Fail to Reject H Reject H
You hear a claim that one fifth of all major-league baseball players were born outside the United States. You take a sample of 75 baseball players and find that 24 of them were born outside the United States. Conduct a hypothesis test to see if your data shows a significant difference from one fifth. Use a significance level of 0.05. a. What should the alternative hypothesis look like? ⒸHA: P > 0.2 ⒸHA: P < 0.2 ⒸHA: P = 0.2 b. Calculate the value of the point estimate. c. Does this meet the success-failure condition? No, we don't have 10 successes and/or we don't have 10 failures Yes, we have at least 10 successes and at least 10 failures. d. Compute the standard error. e. Compute the test statistic. f. What conclusion should we draw regarding H₂? O Fail to Reject H Reject H
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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how do i solve for parts b, d, and e?
![**Hypothesis Testing for Proportion**
You hear a claim that one fifth of all major-league baseball players were born outside the United States. You take a sample of 75 baseball players and find that 24 of them were born outside the United States. Conduct a hypothesis test to see if your data shows a significant difference from one fifth. Use a significance level of 0.05.
**a. What should the alternative hypothesis look like?**
- [ ] \(H_A: p > 0.2\)
- [ ] \(H_A: p < 0.2\)
- [ ] \(H_A: p \neq 0.2\)
**b. Calculate the value of the point estimate.**
_____
**c. Does this meet the success-failure condition?**
- [ ] No, we don't have 10 successes and/or we don't have 10 failures
- [ ] Yes, we have at least 10 successes and at least 10 failures.
**d. Compute the standard error.**
_____
**e. Compute the test statistic.**
_____
**f. What conclusion should we draw regarding \(H_0\)?**
- [ ] Fail to Reject \(H_0\)
- [ ] Reject \(H_0\)
**Explanation of Terms:**
1. **Alternative Hypothesis (\(H_A\))**: This is the hypothesis that you are trying to find evidence for in your sample data. It suggests that there is a difference from the claimed proportion.
2. **Point Estimate**: It is a single value estimate of a population parameter. In this case, it's the sample proportion of baseball players born outside the United States.
3. **Success-Failure Condition**: A condition that states that both the number of successes (24 in this problem) and the number of failures (75 - 24 = 51) should each be at least 10 to use the normal approximation for the sampling distribution of a proportion.
4. **Standard Error**: The standard deviation of the sampling distribution of the sample proportion.
5. **Test Statistic**: A value, calculated from the sample data, that is used in hypothesis testing. It is compared against a threshold to decide whether to reject the null hypothesis.
6. **Conclusion**: Based on the test statistic and the critical value, you will decide whether to reject or fail to reject the null hypothesis \(H_0\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8e28faf-547f-4c48-bb6d-e40546588d1c%2Fc85fec4a-ae24-4664-b823-3de5d66c75ce%2F0g0cyee_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Hypothesis Testing for Proportion**
You hear a claim that one fifth of all major-league baseball players were born outside the United States. You take a sample of 75 baseball players and find that 24 of them were born outside the United States. Conduct a hypothesis test to see if your data shows a significant difference from one fifth. Use a significance level of 0.05.
**a. What should the alternative hypothesis look like?**
- [ ] \(H_A: p > 0.2\)
- [ ] \(H_A: p < 0.2\)
- [ ] \(H_A: p \neq 0.2\)
**b. Calculate the value of the point estimate.**
_____
**c. Does this meet the success-failure condition?**
- [ ] No, we don't have 10 successes and/or we don't have 10 failures
- [ ] Yes, we have at least 10 successes and at least 10 failures.
**d. Compute the standard error.**
_____
**e. Compute the test statistic.**
_____
**f. What conclusion should we draw regarding \(H_0\)?**
- [ ] Fail to Reject \(H_0\)
- [ ] Reject \(H_0\)
**Explanation of Terms:**
1. **Alternative Hypothesis (\(H_A\))**: This is the hypothesis that you are trying to find evidence for in your sample data. It suggests that there is a difference from the claimed proportion.
2. **Point Estimate**: It is a single value estimate of a population parameter. In this case, it's the sample proportion of baseball players born outside the United States.
3. **Success-Failure Condition**: A condition that states that both the number of successes (24 in this problem) and the number of failures (75 - 24 = 51) should each be at least 10 to use the normal approximation for the sampling distribution of a proportion.
4. **Standard Error**: The standard deviation of the sampling distribution of the sample proportion.
5. **Test Statistic**: A value, calculated from the sample data, that is used in hypothesis testing. It is compared against a threshold to decide whether to reject the null hypothesis.
6. **Conclusion**: Based on the test statistic and the critical value, you will decide whether to reject or fail to reject the null hypothesis \(H_0\
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