10. Basic Computation: Testing µ, ☛ Unknown A random sample has 49 values. The sample mean is 8.5 and the sample standard deviation is 1.5. Use a level of significance of 0.01 to conduct a left-tailed test of the claim that the population mean is 9.2. (a) Check Requirements Is it appropriate to use a Student's t distribution? Explain. How many degrees of freedom do we use? (b) What are the hypotheses? (c) Compute the value of the sample test statistic. (d) Estimate the P-value for the test. (e) Do we reject or fail to reject H? (f) Interpret the results.
10. Basic Computation: Testing µ, ☛ Unknown A random sample has 49 values. The sample mean is 8.5 and the sample standard deviation is 1.5. Use a level of significance of 0.01 to conduct a left-tailed test of the claim that the population mean is 9.2. (a) Check Requirements Is it appropriate to use a Student's t distribution? Explain. How many degrees of freedom do we use? (b) What are the hypotheses? (c) Compute the value of the sample test statistic. (d) Estimate the P-value for the test. (e) Do we reject or fail to reject H? (f) Interpret the results.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Please answer number 10. All parts!! Make sure to show work!! Thanks!
![### Basic Computation: Testing μ, σ Unknown
A random sample has 49 values. The sample mean is 8.5 and the sample standard deviation is 1.5. Use a level of significance of 0.01 to conduct a left-tailed test of the claim that the population mean is 9.2.
1. **Check Requirements**
- Is it appropriate to use a Student’s t distribution? Explain.
- How many degrees of freedom do we use?
2. **Hypotheses**
- State the null hypothesis, \( H_0 \), and the alternative hypothesis, \( H_a \).
3. **t Value Calculation**
- Compute the t value of the sample test statistic.
4. **P-Value Estimation**
- Estimate the P-value for the test.
5. **Decision Making**
- Do we reject or fail to reject \( H_0 \)?
6. **Interpretation**
- Interpret the results.
### Steps for Solving the Problem
**(a) Check Requirements**
- **Appropriateness of Student’s t distribution**: Explain the conditions required to use the Student’s t distribution.
- **Degrees of freedom**: Calculate and state the degrees of freedom based on the sample size.
**(b) What Are the Hypotheses?**
- **Null Hypothesis (\( H_0 \))**: The population mean is 9.2.
- **Alternative Hypothesis (\( H_a \))**: The population mean is less than 9.2.
**(c) Compute the t Value**
- **Formula**: Use the formula for the t-test statistic, based on sample mean, population mean, sample standard deviation, and sample size.
\[
t = \frac{\bar{x} - \mu}{s / \sqrt{n}}
\]
**(d) Estimate the P-value**
- **P-value**: Determine the probability of obtaining a test statistic at least as extreme as the one observed, under the assumption that the null hypothesis is true.
**(e) Decision**
- **Reject or Fail to Reject \( H_0 \)**: Compare the P-value with the significance level to make a decision. If the P-value is less than 0.01, reject \( H_0 \).
**(f) Interpret the Results**
- **Conclusion**: Based on the decision in part (](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6805edd-9acc-4ccd-9c7a-22df1558ea0b%2F14dec276-0bcf-4695-a37d-085dd48654da%2F9h740d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Basic Computation: Testing μ, σ Unknown
A random sample has 49 values. The sample mean is 8.5 and the sample standard deviation is 1.5. Use a level of significance of 0.01 to conduct a left-tailed test of the claim that the population mean is 9.2.
1. **Check Requirements**
- Is it appropriate to use a Student’s t distribution? Explain.
- How many degrees of freedom do we use?
2. **Hypotheses**
- State the null hypothesis, \( H_0 \), and the alternative hypothesis, \( H_a \).
3. **t Value Calculation**
- Compute the t value of the sample test statistic.
4. **P-Value Estimation**
- Estimate the P-value for the test.
5. **Decision Making**
- Do we reject or fail to reject \( H_0 \)?
6. **Interpretation**
- Interpret the results.
### Steps for Solving the Problem
**(a) Check Requirements**
- **Appropriateness of Student’s t distribution**: Explain the conditions required to use the Student’s t distribution.
- **Degrees of freedom**: Calculate and state the degrees of freedom based on the sample size.
**(b) What Are the Hypotheses?**
- **Null Hypothesis (\( H_0 \))**: The population mean is 9.2.
- **Alternative Hypothesis (\( H_a \))**: The population mean is less than 9.2.
**(c) Compute the t Value**
- **Formula**: Use the formula for the t-test statistic, based on sample mean, population mean, sample standard deviation, and sample size.
\[
t = \frac{\bar{x} - \mu}{s / \sqrt{n}}
\]
**(d) Estimate the P-value**
- **P-value**: Determine the probability of obtaining a test statistic at least as extreme as the one observed, under the assumption that the null hypothesis is true.
**(e) Decision**
- **Reject or Fail to Reject \( H_0 \)**: Compare the P-value with the significance level to make a decision. If the P-value is less than 0.01, reject \( H_0 \).
**(f) Interpret the Results**
- **Conclusion**: Based on the decision in part (
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 1 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman