You wish to test the following claim (H) at a significance level of α = 0.001. Ho:μ = 88.1 Η„: μ # 88.1 You believe the population is normally distributed, but you do not know the standard deviation. You a a sample of size n = 19 with a mean of M = 80.2 and a standard deviation of SD = 18.2. 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 =

MATLAB: An Introduction with Applications
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### Hypothesis Testing: Example Scenario

You wish to test the following claim (\(H_a\)) at a significance level of \(\alpha = 0.001\).

\[
H_0: \mu = 88.1 \\
H_a: \mu \neq 88.1
\]

#### Sample Information

- Population is assumed to be normally distributed.
- Sample size (\(n\)) = 19
- Sample mean (\(M\)) = 80.2
- Sample standard deviation (\(SD\)) = 18.2

### Questions

1. **What is the critical value for this test?**  
   - Report your answer accurate to three decimal places.
   - **Critical Value = ± [ ___ ]**

2. **What is the test statistic for this sample?**  
   - Report your answer accurate to three decimal places.
   - **Test Statistic = [ ___ ]**

3. **The test statistic is...**
   - ( ) in the critical region
   - ( ) not in the critical region

4. **This test statistic leads to a decision to...**
   - ( ) reject the null
   - ( ) accept the null
   - ( ) fail to reject the null

### Instructions

Please calculate the critical value and the test statistic using the given sample data. Use these values to determine whether the test statistic falls within the critical region. Make a decision based on the statistical evidence regarding the null hypothesis.
Transcribed Image Text:### Hypothesis Testing: Example Scenario You wish to test the following claim (\(H_a\)) at a significance level of \(\alpha = 0.001\). \[ H_0: \mu = 88.1 \\ H_a: \mu \neq 88.1 \] #### Sample Information - Population is assumed to be normally distributed. - Sample size (\(n\)) = 19 - Sample mean (\(M\)) = 80.2 - Sample standard deviation (\(SD\)) = 18.2 ### Questions 1. **What is the critical value for this test?** - Report your answer accurate to three decimal places. - **Critical Value = ± [ ___ ]** 2. **What is the test statistic for this sample?** - Report your answer accurate to three decimal places. - **Test Statistic = [ ___ ]** 3. **The test statistic is...** - ( ) in the critical region - ( ) not in the critical region 4. **This test statistic leads to a decision to...** - ( ) reject the null - ( ) accept the null - ( ) fail to reject the null ### Instructions Please calculate the critical value and the test statistic using the given sample data. Use these values to determine whether the test statistic falls within the critical region. Make a decision based on the statistical evidence regarding the null hypothesis.
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