Please answer number 10. All parts!! Make sure to show work!! Thanks! ### Basic Computation: Testing μ, σ UnknownA 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 (

the one-sample t-test:The one-sample t-test is a statistical hypothesis test used to determine…

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

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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 (

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