In a test of the hypothesis Ho: µ= 10 versus Ha: u # 10, a sample of n= 50 observations possessed mean x = 10.7 and standard deviation s = 2.9. Find and interpret the p-value for this test. The p-value for this test is (Round to four decimal places as needed.) Interpret the result. Choose the correct answer below. O A. There is sufficient evidence to reject Ho for a>0.09. O B. There is sufficient evidence to reject Ho for a< 0.09. OC. There is insufficient evidence to reject Ho for a = 0.15. O D. There is insufficient evidence to reject Ho for a> 0.09.
In a test of the hypothesis Ho: µ= 10 versus Ha: u # 10, a sample of n= 50 observations possessed mean x = 10.7 and standard deviation s = 2.9. Find and interpret the p-value for this test. The p-value for this test is (Round to four decimal places as needed.) Interpret the result. Choose the correct answer below. O A. There is sufficient evidence to reject Ho for a>0.09. O B. There is sufficient evidence to reject Ho for a< 0.09. OC. There is insufficient evidence to reject Ho for a = 0.15. O D. There is insufficient evidence to reject Ho for a> 0.09.
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Question
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In a test of the hypothesis
H0: μ=10
versus
Ha: μ≠10,
a sample of
n=50
observations possessed mean
x=10.7
and standard deviation
s=2.9.
Find and interpret the p-value for this test.(Solve all)
![### Hypothesis Testing Example
In a test of the hypothesis \( H_0: \mu = 10 \) versus \( H_a: \mu \neq 10 \), a sample of \( n = 50 \) observations possessed mean \( \bar{x} = 10.7 \) and standard deviation \( s = 2.9 \). Find and interpret the p-value for this test.
1. **Step 1: Calculate the test statistic**
\[
t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}
\]
where \( \bar{x} = 10.7 \), \( \mu_0 = 10 \), \( s = 2.9 \), and \( n = 50 \).
2. **Step 2: Determine the p-value**
Calculate the p-value from the test statistic using the appropriate distribution (t-distribution with \( n - 1 \) degrees of freedom).
3. **Next, you are required to fill in the calculated p-value:**
\[
\text{The p-value for this test is } \_\_\_\_ . \text{ (Round to four decimal places as needed.)}
\]
4. **Step 3: Interpret the result. Choose the correct answer below:**
\[
\text{A. There is sufficient evidence to reject } H_0 \text{ for } \alpha > 0.09.
\]
\[
\text{B. There is sufficient evidence to reject } H_0 \text{ for } \alpha < 0.09.
\]
\[
\text{C. There is insufficient evidence to reject } H_0 \text{ for } \alpha = 0.15.
\]
\[
\text{D. There is insufficient evidence to reject } H_0 \text{ for } \alpha > 0.09.
\]
**Explanation:**
- Choice **A** is correctly selected on the screen, indicating that the p-value calculated is greater than 0.09, suggesting that there is sufficient evidence to reject the null hypothesis \( H_0 \) when the significance level \( \alpha \) is greater than 0.09.
- Each choice reflects a possible interpretation of the p-value in relation to the significance level \(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d6ce828-7421-4579-a347-7b809a44673d%2F83469fc7-c0e0-4dff-b61e-1b912888cf66%2Fqx3vwa5_processed.png&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing Example
In a test of the hypothesis \( H_0: \mu = 10 \) versus \( H_a: \mu \neq 10 \), a sample of \( n = 50 \) observations possessed mean \( \bar{x} = 10.7 \) and standard deviation \( s = 2.9 \). Find and interpret the p-value for this test.
1. **Step 1: Calculate the test statistic**
\[
t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}
\]
where \( \bar{x} = 10.7 \), \( \mu_0 = 10 \), \( s = 2.9 \), and \( n = 50 \).
2. **Step 2: Determine the p-value**
Calculate the p-value from the test statistic using the appropriate distribution (t-distribution with \( n - 1 \) degrees of freedom).
3. **Next, you are required to fill in the calculated p-value:**
\[
\text{The p-value for this test is } \_\_\_\_ . \text{ (Round to four decimal places as needed.)}
\]
4. **Step 3: Interpret the result. Choose the correct answer below:**
\[
\text{A. There is sufficient evidence to reject } H_0 \text{ for } \alpha > 0.09.
\]
\[
\text{B. There is sufficient evidence to reject } H_0 \text{ for } \alpha < 0.09.
\]
\[
\text{C. There is insufficient evidence to reject } H_0 \text{ for } \alpha = 0.15.
\]
\[
\text{D. There is insufficient evidence to reject } H_0 \text{ for } \alpha > 0.09.
\]
**Explanation:**
- Choice **A** is correctly selected on the screen, indicating that the p-value calculated is greater than 0.09, suggesting that there is sufficient evidence to reject the null hypothesis \( H_0 \) when the significance level \( \alpha \) is greater than 0.09.
- Each choice reflects a possible interpretation of the p-value in relation to the significance level \(
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