You wish to test the following claim (Ha) at a significance level of a = 0.005. Ho: μ = 71.5 Ha: μ > 71.5 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 529 with a mean of M = 72.9 and a standard deviation of SD = 18.3. What is the critical value for this test? (Report answer accurate to three decimal places.) critical value = What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = The test statistic is... O in the critical region O not in the critical region This test statistic leads to a decision to... O reject the null O accept the null O fail to reject the null As such, the final conclusion is that... O There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 71.5. O There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 71.5. O The sample data support the claim that the population mean is greater than 71.5. O There is not sufficient sample evidence to support the claim that the population mean is greater than 71.5.
You wish to test the following claim (Ha) at a significance level of a = 0.005. Ho: μ = 71.5 Ha: μ > 71.5 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 529 with a mean of M = 72.9 and a standard deviation of SD = 18.3. What is the critical value for this test? (Report answer accurate to three decimal places.) critical value = What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = The test statistic is... O in the critical region O not in the critical region This test statistic leads to a decision to... O reject the null O accept the null O fail to reject the null As such, the final conclusion is that... O There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 71.5. O There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 71.5. O The sample data support the claim that the population mean is greater than 71.5. O There is not sufficient sample evidence to support the claim that the population mean is greater than 71.5.
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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![### Hypothesis Testing with Unknown Population Standard Deviation
#### Testing a Claim about a Population Mean (\(H_a\)) at a Significance Level of \(\alpha = 0.005\)
Given Hypotheses:
- Null Hypothesis: \(H_0: \mu = 71.5\)
- Alternative Hypothesis: \(H_a: \mu > 71.5\)
#### Sample Data
- Sample size (\(n\)): 529
- Sample mean (\(M\)): 72.9
- Sample standard deviation (\(SD\)): 18.3
### Critical Value Calculation
To find the critical value for this one-tailed test at a significance level of \(\alpha = 0.005\), one would typically refer to statistical tables or use statistical software.
#### Test Statistic Calculation
The test statistic for the sample is calculated using the formula:
\[ \text{Test statistic (t)} = \frac{M - \mu}{(SD/\sqrt{n})} \]
Here:
- \( \mu \) is the population mean under the null hypothesis.
- \( M \) is the sample mean.
- \( SD \) is the sample standard deviation.
- \( n \) is the sample size.
### Decision Rule
Determine the critical value and compare the test statistic to the critical region.
- **The test statistic is...**
- \( \square \) in the critical region
- \( \squircle \) not in the critical region
Based on whether the test statistic falls within the critical region, proceed to make a decision.
### Conclusion
The decision will lead to one of the following conclusions:
- **This test statistic leads to a decision to...**
- \( \bigcirc \) reject the null
- \( \square \) accept the null
- \( \squircle \) fail to reject the null
Then, make the final conclusion based on your decision:
- **As such, the final conclusion is that…**
- \( \bigcirc \) There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 71.5.
- \( \square \) There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 71.5.
- \( \squircle \) The sample data support the claim that the population mean is greater](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2539764-cbb6-4f84-96a1-bc799fc276f3%2Fe4089c5c-e20b-4df6-a307-1aaa2faea56d%2F74n6xrp_processed.png&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing with Unknown Population Standard Deviation
#### Testing a Claim about a Population Mean (\(H_a\)) at a Significance Level of \(\alpha = 0.005\)
Given Hypotheses:
- Null Hypothesis: \(H_0: \mu = 71.5\)
- Alternative Hypothesis: \(H_a: \mu > 71.5\)
#### Sample Data
- Sample size (\(n\)): 529
- Sample mean (\(M\)): 72.9
- Sample standard deviation (\(SD\)): 18.3
### Critical Value Calculation
To find the critical value for this one-tailed test at a significance level of \(\alpha = 0.005\), one would typically refer to statistical tables or use statistical software.
#### Test Statistic Calculation
The test statistic for the sample is calculated using the formula:
\[ \text{Test statistic (t)} = \frac{M - \mu}{(SD/\sqrt{n})} \]
Here:
- \( \mu \) is the population mean under the null hypothesis.
- \( M \) is the sample mean.
- \( SD \) is the sample standard deviation.
- \( n \) is the sample size.
### Decision Rule
Determine the critical value and compare the test statistic to the critical region.
- **The test statistic is...**
- \( \square \) in the critical region
- \( \squircle \) not in the critical region
Based on whether the test statistic falls within the critical region, proceed to make a decision.
### Conclusion
The decision will lead to one of the following conclusions:
- **This test statistic leads to a decision to...**
- \( \bigcirc \) reject the null
- \( \square \) accept the null
- \( \squircle \) fail to reject the null
Then, make the final conclusion based on your decision:
- **As such, the final conclusion is that…**
- \( \bigcirc \) There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 71.5.
- \( \square \) There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 71.5.
- \( \squircle \) The sample data support the claim that the population mean is greater
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