Ho: μ ≤ 12 H₂: μ> 12 A sample of 25 provided a sample mean x = 14 and a sample standard deviation s = 4.44. (a) Compute the value of the test statistic. (Round your answer to three decimal places.) (b) Use the t distribution table to compute a range for the p-value. O p-value > 0.200 0.100 < p-value < 0.200 O 0.050 < p-value < 0.100 O 0.025 < p-value < 0.050 O 0.010 < p-value < 0.025 O p-value < 0.010 (c) At a = 0.05, what is your conclusion? O Do not reject Ho. There is insufficient evidence to conclude that μ > 12. O Reject Ho. There is sufficient evidence to conclude that μ > 12. O Reject Ho. There is insufficient evidence to conclude that μ > 12. O Do not reject Ho. There is sufficient evidence to conclude that μ > 12.
Ho: μ ≤ 12 H₂: μ> 12 A sample of 25 provided a sample mean x = 14 and a sample standard deviation s = 4.44. (a) Compute the value of the test statistic. (Round your answer to three decimal places.) (b) Use the t distribution table to compute a range for the p-value. O p-value > 0.200 0.100 < p-value < 0.200 O 0.050 < p-value < 0.100 O 0.025 < p-value < 0.050 O 0.010 < p-value < 0.025 O p-value < 0.010 (c) At a = 0.05, what is your conclusion? O Do not reject Ho. There is insufficient evidence to conclude that μ > 12. O Reject Ho. There is sufficient evidence to conclude that μ > 12. O Reject Ho. There is insufficient evidence to conclude that μ > 12. O Do not reject Ho. There is sufficient evidence to conclude that μ > 12.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![## Hypothesis Testing Example
### Given Hypotheses
- **Null Hypothesis:** \( H_{0}: \mu \leq 12 \)
- **Alternative Hypothesis:** \( H_{a}: \mu > 12 \)
### Sample Data
A sample of 25 provided a sample mean \( \overline{x} = 14 \) and a sample standard deviation \( s = 4.44 \).
### (a) Compute the value of the test statistic
Compute the value of the test statistic. (Round your answer to three decimal places.)
\[ \text{Test Statistic:} \ \underline{\hspace{50px}} \]
### (b) Use the t distribution table to compute a range for the p-value
Select the range for the p-value:
- \(\circ\) \( p\text{-value} > 0.200 \)
- \(\circ\) \( 0.100 < p\text{-value} < 0.200 \)
- \(\circ\) \( 0.050 < p\text{-value} < 0.100 \)
- \(\circ\) \( 0.025 < p\text{-value} < 0.050 \)
- \(\circ\) \( 0.010 < p\text{-value} < 0.025 \)
- \(\circ\) \( p\text{-value} < 0.010 \)
### (c) Conclusion at \( \alpha = 0.05 \)
What is your conclusion at \( \alpha = 0.05 \)?
- \(\circ\) Do not reject \( H_{0} \). There is insufficient evidence to conclude that \( \mu > 12 \).
- \(\circ\) Reject \( H_{0} \). There is sufficient evidence to conclude that \( \mu > 12 \).
- \(\circ\) Reject \( H_{0} \). There is insufficient evidence to conclude that \( \mu > 12 \).
- \(\circ\) Do not reject \( H_{0} \). There is sufficient evidence to conclude that \( \mu > 12 \).
### (d) Rejection Rule Using Critical Value
What is the rejection rule using the critical value? (If the test is one-tailed, enter NONE for the unused tail. Round your answer](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98fd5880-bd7f-4b90-9f43-35abbd9a1544%2Fe287ee74-c766-4190-badf-23179164f318%2Fbzdyn9r_processed.png&w=3840&q=75)
Transcribed Image Text:## Hypothesis Testing Example
### Given Hypotheses
- **Null Hypothesis:** \( H_{0}: \mu \leq 12 \)
- **Alternative Hypothesis:** \( H_{a}: \mu > 12 \)
### Sample Data
A sample of 25 provided a sample mean \( \overline{x} = 14 \) and a sample standard deviation \( s = 4.44 \).
### (a) Compute the value of the test statistic
Compute the value of the test statistic. (Round your answer to three decimal places.)
\[ \text{Test Statistic:} \ \underline{\hspace{50px}} \]
### (b) Use the t distribution table to compute a range for the p-value
Select the range for the p-value:
- \(\circ\) \( p\text{-value} > 0.200 \)
- \(\circ\) \( 0.100 < p\text{-value} < 0.200 \)
- \(\circ\) \( 0.050 < p\text{-value} < 0.100 \)
- \(\circ\) \( 0.025 < p\text{-value} < 0.050 \)
- \(\circ\) \( 0.010 < p\text{-value} < 0.025 \)
- \(\circ\) \( p\text{-value} < 0.010 \)
### (c) Conclusion at \( \alpha = 0.05 \)
What is your conclusion at \( \alpha = 0.05 \)?
- \(\circ\) Do not reject \( H_{0} \). There is insufficient evidence to conclude that \( \mu > 12 \).
- \(\circ\) Reject \( H_{0} \). There is sufficient evidence to conclude that \( \mu > 12 \).
- \(\circ\) Reject \( H_{0} \). There is insufficient evidence to conclude that \( \mu > 12 \).
- \(\circ\) Do not reject \( H_{0} \). There is sufficient evidence to conclude that \( \mu > 12 \).
### (d) Rejection Rule Using Critical Value
What is the rejection rule using the critical value? (If the test is one-tailed, enter NONE for the unused tail. Round your answer
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