You wish to test the following claim (Ha) at a significance level of a = 0.10. H,:µ = 89.2 HaiH > 89.2 You believe the population is normally distributed and you know the standard deviation is a = 10.7 .You obtain a sample mean of M = 93.4 for a sample of size n = 23. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic - What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is. O less than (or equal to) a O greater than a 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 89.2. O There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 89.2. O The sample data support the claim that the population mean is greater than 89.2. O There is not sufficient sample evidence to support the claim that the population mean is greater than 89.2.
You wish to test the following claim (Ha) at a significance level of a = 0.10. H,:µ = 89.2 HaiH > 89.2 You believe the population is normally distributed and you know the standard deviation is a = 10.7 .You obtain a sample mean of M = 93.4 for a sample of size n = 23. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic - What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is. O less than (or equal to) a O greater than a 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 89.2. O There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 89.2. O The sample data support the claim that the population mean is greater than 89.2. O There is not sufficient sample evidence to support the claim that the population mean is greater than 89.2.
MATLAB: An Introduction with Applications
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Chapter1: Starting With Matlab
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Question
![**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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F010d10ea-7975-4510-a7a7-5e4f696daa17%2F5035a699-e0f5-48d3-b0a2-e270087bc202%2Fxphilxl_processed.png&w=3840&q=75)
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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