MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![**Hypothesis Testing at Significance Level 0.10**
**Claim (Hₐ):**
\( H_0: \mu = 89.2 \\
H_a: \mu > 89.2 \)
**Given Data:**
- Population is normally distributed.
- Standard deviation \( \sigma = 10.7 \).
- Sample mean \( \bar{X} = 93.4 \).
- Sample size \( n = 23 \).
**Tasks:**
1. **Calculate the Test Statistic:**
- Use the formula for the test statistic for a one-sample z-test:
\[
z = \frac{\bar{X} - \mu}{\sigma/\sqrt{n}}
\]
- Substitute the given values:
\[
z = \frac{93.4 - 89.2}{10.7/\sqrt{23}}
\]
- Compute the value and report the test statistic accurate to three decimal places.
2. **Determine the p-value:**
- Based on the calculated z-value, find the corresponding p-value from the standard normal distribution.
- Report the p-value accurate to four decimal places.
3. **Compare p-value with α:**
- The p-value is either less than (or equal to) α or greater than α.
4. **Choose the Statistical Decision:**
- Depending on the comparison of the p-value with α, decide to either reject the null hypothesis, accept the null hypothesis, or fail to reject the null hypothesis.
**Conclusion:**
- Make the final conclusion about the population mean based on the decision:
- If you reject the null hypothesis, there is sufficient evidence to support that the population mean is greater than 89.2.
- If you fail to reject the null hypothesis, there is not sufficient evidence to support that the population mean is greater than 89.2.
**Conclusion Options:**
- There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 89.2.
- There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 89.2.
- The sample data support the claim that the population mean is greater than 89.2.
- There is not sufficient sample evidence to support the claim that the population mean is greater than 89.2.](https://content.bartleby.com/qna-images/question/010d10ea-7975-4510-a7a7-5e4f696daa17/5035a699-e0f5-48d3-b0a2-e270087bc202/xphilxl_processed.png)
Transcribed Image Text:**Hypothesis Testing at Significance Level 0.10**
**Claim (Hₐ):**
\( H_0: \mu = 89.2 \\
H_a: \mu > 89.2 \)
**Given Data:**
- Population is normally distributed.
- Standard deviation \( \sigma = 10.7 \).
- Sample mean \( \bar{X} = 93.4 \).
- Sample size \( n = 23 \).
**Tasks:**
1. **Calculate the Test Statistic:**
- Use the formula for the test statistic for a one-sample z-test:
\[
z = \frac{\bar{X} - \mu}{\sigma/\sqrt{n}}
\]
- Substitute the given values:
\[
z = \frac{93.4 - 89.2}{10.7/\sqrt{23}}
\]
- Compute the value and report the test statistic accurate to three decimal places.
2. **Determine the p-value:**
- Based on the calculated z-value, find the corresponding p-value from the standard normal distribution.
- Report the p-value accurate to four decimal places.
3. **Compare p-value with α:**
- The p-value is either less than (or equal to) α or greater than α.
4. **Choose the Statistical Decision:**
- Depending on the comparison of the p-value with α, decide to either reject the null hypothesis, accept the null hypothesis, or fail to reject the null hypothesis.
**Conclusion:**
- Make the final conclusion about the population mean based on the decision:
- If you reject the null hypothesis, there is sufficient evidence to support that the population mean is greater than 89.2.
- If you fail to reject the null hypothesis, there is not sufficient evidence to support that the population mean is greater than 89.2.
**Conclusion Options:**
- There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 89.2.
- There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 89.2.
- The sample data support the claim that the population mean is greater than 89.2.
- There is not sufficient sample evidence to support the claim that the population mean is greater than 89.2.
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