You wish to test the following claim (H) at a significance level of a = 0.005. Ho: 55.9 Ha: 55.9 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 686 with a mean of M = 54.9 and a standard deviation of SD = 8.3. 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... There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 55.9. O There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 55.9. The sample data support the claim that the population mean is not equal to 55.9. There is not sufficient sample evidence to support the claim that the population mean is not equal to 55.9.

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**Hypothesis Testing Tutorial**

You wish to test the following claim (\(H_a\)) at a significance level of \(\alpha = 0.005\).

- \(H_0: \mu = 55.9\)
- \(H_a: \mu \neq 55.9\)

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size \(n = 686\) with a mean of \(M = 54.9\) and a standard deviation of \(SD = 8.3\).

**Question 1: Critical Value for the Test**

What is the critical value for this test? (Report answer accurate to three decimal places.)

- Critical value = ± [input box]

**Question 2: Test Statistic for the Sample**

What is the test statistic for this sample? (Report answer accurate to three decimal places.)

- Test statistic = [input box]

**Determine the Test Statistic's Significance**

The test statistic is...
- [ ] In the critical region
- [ ] Not in the critical region

**Decision on Hypotheses**

This test statistic leads to a decision to...
- [ ] Reject the null
- [ ] Accept the null
- [ ] Fail to reject the null

**Final Conclusion**

As such, the final conclusion is that...
- [ ] There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 55.9.
- [ ] There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 55.9.
- [ ] The sample data support the claim that the population mean is not equal to 55.9.
- [ ] There is not sufficient sample evidence to support the claim that the population mean is not equal to 55.9.

*Please calculate and fill in the appropriate values to complete this hypothesis testing practice.*
Transcribed Image Text:**Hypothesis Testing Tutorial** You wish to test the following claim (\(H_a\)) at a significance level of \(\alpha = 0.005\). - \(H_0: \mu = 55.9\) - \(H_a: \mu \neq 55.9\) You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size \(n = 686\) with a mean of \(M = 54.9\) and a standard deviation of \(SD = 8.3\). **Question 1: Critical Value for the Test** What is the critical value for this test? (Report answer accurate to three decimal places.) - Critical value = ± [input box] **Question 2: Test Statistic for the Sample** What is the test statistic for this sample? (Report answer accurate to three decimal places.) - Test statistic = [input box] **Determine the Test Statistic's Significance** The test statistic is... - [ ] In the critical region - [ ] Not in the critical region **Decision on Hypotheses** This test statistic leads to a decision to... - [ ] Reject the null - [ ] Accept the null - [ ] Fail to reject the null **Final Conclusion** As such, the final conclusion is that... - [ ] There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 55.9. - [ ] There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 55.9. - [ ] The sample data support the claim that the population mean is not equal to 55.9. - [ ] There is not sufficient sample evidence to support the claim that the population mean is not equal to 55.9. *Please calculate and fill in the appropriate values to complete this hypothesis testing practice.*
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