Consider the following hypothesis test. Ho: ≤ 12 H₂: > 12 A sample of 25 provided a sample mean x = 14 and a sample standard deviation s = 4.52. (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. Op-value > 0.200 O 0.100 < p-value < 0.200 0.050 < p-value < 0.100 0.025 < p-value < 0.050 0.010 < p-value < 0.025 Op-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. Do not reject Ho. There is sufficient evidence to conclude that μ> 12. Reject Ho. There is insufficient evidence to conclude that μ> 12.
Consider the following hypothesis test. Ho: ≤ 12 H₂: > 12 A sample of 25 provided a sample mean x = 14 and a sample standard deviation s = 4.52. (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. Op-value > 0.200 O 0.100 < p-value < 0.200 0.050 < p-value < 0.100 0.025 < p-value < 0.050 0.010 < p-value < 0.025 Op-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. Do not reject Ho. There is sufficient evidence to conclude that μ> 12. Reject Ho. There is insufficient 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 Guide
#### Problem Statement
Consider the following hypothesis test:
- Null Hypothesis (H0): μ ≤ 12
- Alternative Hypothesis (Ha): μ > 12
A sample of 25 provided a sample mean (\(\bar{x}\)) = 14 and a sample standard deviation (s) = 4.52.
#### Steps to Solve
**(a) Compute the value of the test statistic.**
- Use the formula for the test statistic for a one-sample t-test:
\[ t = \frac{\bar{x} - \mu}{s / \sqrt{n}} \]
- Here, \(\bar{x}\) is the sample mean, \(\mu\) is the hypothesized population mean, \(s\) is the sample standard deviation, and \(n\) is the sample size. Plug in the provided values and round off your answer to three decimal places.
**(b) Use the t distribution table to compute a range for the p-value.**
- Based on the calculated test statistic in part (a), refer to the t distribution table to determine the range where the p-value falls.
- Select the appropriate range:
- \( \text{p-value} > 0.200 \)
- \( 0.100 < \text{p-value} < 0.200 \)
- \( 0.050 < \text{p-value} < 0.100 \)
- \( 0.025 < \text{p-value} < 0.050 \)
- \( 0.010 < \text{p-value} < 0.025 \)
- \( \text{p-value} < 0.010 \)
**(c) At α = 0.05, what is your conclusion?**
- Based on the computed p-value range in part (b), decide whether to reject or not reject the null hypothesis at the significance level (α) of 0.05.
- Possible conclusions:
- \( \circ \) 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 \( \mu > 12 \).
- \( \circ \) Do not reject \( H_0 \). There is sufficient evidence to conclude that](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa4ed8498-f2f2-4dcb-bcb0-3b3cd025dd21%2Fbd8c4573-373b-41f7-9527-747e97897537%2Fkhep7zr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing Guide
#### Problem Statement
Consider the following hypothesis test:
- Null Hypothesis (H0): μ ≤ 12
- Alternative Hypothesis (Ha): μ > 12
A sample of 25 provided a sample mean (\(\bar{x}\)) = 14 and a sample standard deviation (s) = 4.52.
#### Steps to Solve
**(a) Compute the value of the test statistic.**
- Use the formula for the test statistic for a one-sample t-test:
\[ t = \frac{\bar{x} - \mu}{s / \sqrt{n}} \]
- Here, \(\bar{x}\) is the sample mean, \(\mu\) is the hypothesized population mean, \(s\) is the sample standard deviation, and \(n\) is the sample size. Plug in the provided values and round off your answer to three decimal places.
**(b) Use the t distribution table to compute a range for the p-value.**
- Based on the calculated test statistic in part (a), refer to the t distribution table to determine the range where the p-value falls.
- Select the appropriate range:
- \( \text{p-value} > 0.200 \)
- \( 0.100 < \text{p-value} < 0.200 \)
- \( 0.050 < \text{p-value} < 0.100 \)
- \( 0.025 < \text{p-value} < 0.050 \)
- \( 0.010 < \text{p-value} < 0.025 \)
- \( \text{p-value} < 0.010 \)
**(c) At α = 0.05, what is your conclusion?**
- Based on the computed p-value range in part (b), decide whether to reject or not reject the null hypothesis at the significance level (α) of 0.05.
- Possible conclusions:
- \( \circ \) 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 \( \mu > 12 \).
- \( \circ \) Do not reject \( H_0 \). There is sufficient evidence to conclude that
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