A sample mean, sample size, and sample standard deviation are provided below. Use the one-mean t-test to perform the required hypothesis test at the 5% significance level. x=25, s=4, n=24, Ho: H=25, H₂: μ#25 Click here to view a partial table of values of t The test statistic is t= (Round to two decimal places as needed)
A sample mean, sample size, and sample standard deviation are provided below. Use the one-mean t-test to perform the required hypothesis test at the 5% significance level. x=25, s=4, n=24, Ho: H=25, H₂: μ#25 Click here to view a partial table of values of t The test statistic is t= (Round to two decimal places as needed)
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
Need to solve this three questions
the last one is reject or not
provide or not
less than, not equal, greater than, equal
![## One-Mean T-Test Calculation Tutorial
### Problem Statement
A sample mean, sample size, and sample standard deviation are provided below. Use the one-mean t-test to perform the required hypothesis test at the 5% significance level.
#### Given Data:
- Sample mean (\(\bar{x}\)): 25
- Sample standard deviation (\(s\)): 4
- Sample size (\(n\)): 24
- Null hypothesis (\(H_0\)): \(\mu = 25\)
- Alternative hypothesis (\(H_a\)): \(\mu \neq 25\)
[Click here to view a partial table of values of \(t_\alpha\).]
### Steps to Calculate the Test Statistic
**Formula:**
\[
t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}
\]
**Instructions:**
1. Plug in the given values into the formula.
2. Calculate the t-value.
3. Round the final result to two decimal places as needed.
**Calculation:**
\[
t = \frac{25 - 25}{\frac{4}{\sqrt{24}}}
\]
**Result:**
- The test statistic \(t\) is [Fill in the blank].
- (Round to two decimal places as needed.)
---
### Note:
- Ensure that you compare the calculated t-value with the critical t-value from the t-distribution table to make the decision regarding the null hypothesis (\(H_0\)).
- Use the partial table of values of \(t_\alpha\) for critical values based on your degree of freedom (df).
This tutorial helps in understanding and performing the one-mean t-test for hypothesis testing.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b33feb0-e62b-4e25-aad1-2d23e491b0f1%2F348bc706-4c35-40ea-8170-625204f40ff1%2F2w6iab_processed.png&w=3840&q=75)
Transcribed Image Text:## One-Mean T-Test Calculation Tutorial
### Problem Statement
A sample mean, sample size, and sample standard deviation are provided below. Use the one-mean t-test to perform the required hypothesis test at the 5% significance level.
#### Given Data:
- Sample mean (\(\bar{x}\)): 25
- Sample standard deviation (\(s\)): 4
- Sample size (\(n\)): 24
- Null hypothesis (\(H_0\)): \(\mu = 25\)
- Alternative hypothesis (\(H_a\)): \(\mu \neq 25\)
[Click here to view a partial table of values of \(t_\alpha\).]
### Steps to Calculate the Test Statistic
**Formula:**
\[
t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}
\]
**Instructions:**
1. Plug in the given values into the formula.
2. Calculate the t-value.
3. Round the final result to two decimal places as needed.
**Calculation:**
\[
t = \frac{25 - 25}{\frac{4}{\sqrt{24}}}
\]
**Result:**
- The test statistic \(t\) is [Fill in the blank].
- (Round to two decimal places as needed.)
---
### Note:
- Ensure that you compare the calculated t-value with the critical t-value from the t-distribution table to make the decision regarding the null hypothesis (\(H_0\)).
- Use the partial table of values of \(t_\alpha\) for critical values based on your degree of freedom (df).
This tutorial helps in understanding and performing the one-mean t-test for hypothesis testing.
![### Hypothesis Testing - Critical Values and Decisions
#### Test Statistic
The test statistic is \( t = 2.58 \).
*(Round to two decimal places as needed.)*
#### Critical Value(s)
Identify the critical value(s). Select the correct choice below and fill in the answer box within your choice.
*(Round to three decimal places as needed.)*
- **A.** The critical value is \( -t_{\alpha} = \_\_\_\_\_\_\_\_ \) .
- **B.** The critical value is \( t_{\alpha} = \_\_\_\_\_\_\_\_ \) .
- **C.** The critical values are \( \pm t_{\alpha / 2} = \pm 1.761 \).
#### Hypothesis Decision
\[ \boxed{\text{Fail to reject}} \] the null hypothesis. The data \[ \boxed{\text{do not provide}} \] sufficient evidence to conclude that the mean is \[ \boxed{\text{greater than}} \] .](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b33feb0-e62b-4e25-aad1-2d23e491b0f1%2F348bc706-4c35-40ea-8170-625204f40ff1%2F8k237cb_processed.png&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing - Critical Values and Decisions
#### Test Statistic
The test statistic is \( t = 2.58 \).
*(Round to two decimal places as needed.)*
#### Critical Value(s)
Identify the critical value(s). Select the correct choice below and fill in the answer box within your choice.
*(Round to three decimal places as needed.)*
- **A.** The critical value is \( -t_{\alpha} = \_\_\_\_\_\_\_\_ \) .
- **B.** The critical value is \( t_{\alpha} = \_\_\_\_\_\_\_\_ \) .
- **C.** The critical values are \( \pm t_{\alpha / 2} = \pm 1.761 \).
#### Hypothesis Decision
\[ \boxed{\text{Fail to reject}} \] the null hypothesis. The data \[ \boxed{\text{do not provide}} \] sufficient evidence to conclude that the mean is \[ \boxed{\text{greater than}} \] .
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