The mean score on a 25-point placement exam in mathematics used for the past two years at a large state university is 14.3. The placement coordinator wishes to test whether the mean score on a revised version of the exam differs from 14.3. She gives the revised exam to 20 entering freshmen early in the summer; the mean score is 14.6 with standard deviation 2.4.
The mean score on a 25-point placement exam in mathematics used for the past two years at a large state university is 14.3. The placement coordinator wishes to test whether the mean score on a revised version of the exam differs from 14.3. She gives the revised exam to 20 entering freshmen early in the summer; the mean score is 14.6 with standard deviation 2.4.
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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I only need help with the second part of the question that is in the screenshot sent/posted. I'm not sure what I should write as my conclusion since I need to tie it in with the question.
![### Problem Statement
The mean score on a 25-point placement exam in mathematics used for the past two years at a large state university is 14.3. The placement coordinator wishes to test whether the mean score on a revised version of the exam differs from 14.3. She gives the revised exam to 20 entering freshmen early in the summer; the mean score is 14.6 with a standard deviation of 2.4.
#### Tasks:
a. Perform the test at the 10% level of significance using the critical value approach.
b. Perform the test at the 10% level of significance using the p-value approach.
### Solution
To solve this problem, we will conduct a hypothesis test for the mean score using both the critical value approach and the p-value approach.
#### Steps to solve:
1. **State the hypotheses:**
- Null hypothesis (H₀): µ = 14.3 (The mean score is 14.3)
- Alternative hypothesis (H₁): µ ≠ 14.3 (The mean score is different from 14.3)
2. **Choose the significance level (α):**
- Significance level (α) = 0.10
3. **Calculate the test statistic:**
- We will use the t-test since the sample size (n = 20) is small.
- The test statistic is calculated using the formula:
\[
t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}
\]
Where:
- \(\bar{x}\) = sample mean = 14.6
- \(\mu_0\) = population mean = 14.3
- \(s\) = sample standard deviation = 2.4
- \(n\) = sample size = 20
4. **Determine the critical value:**
- For a two-tailed test at α = 0.10, the critical values for t with (n-1) degrees of freedom (df = 20 - 1 = 19) are approximately ±1.729.
5. **Decision (Critical Value Approach):**
- If the test statistic falls outside the range of -1.729 to 1.729, we reject the null hypothesis.
6. **Decision (p-value Approach):**
- Calculate the p-value associated](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F60837528-6200-4f82-a967-681bd5edb89a%2Ff9db0f4a-c8b9-4399-af5f-8ee29af4578f%2Fc2osuy.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement
The mean score on a 25-point placement exam in mathematics used for the past two years at a large state university is 14.3. The placement coordinator wishes to test whether the mean score on a revised version of the exam differs from 14.3. She gives the revised exam to 20 entering freshmen early in the summer; the mean score is 14.6 with a standard deviation of 2.4.
#### Tasks:
a. Perform the test at the 10% level of significance using the critical value approach.
b. Perform the test at the 10% level of significance using the p-value approach.
### Solution
To solve this problem, we will conduct a hypothesis test for the mean score using both the critical value approach and the p-value approach.
#### Steps to solve:
1. **State the hypotheses:**
- Null hypothesis (H₀): µ = 14.3 (The mean score is 14.3)
- Alternative hypothesis (H₁): µ ≠ 14.3 (The mean score is different from 14.3)
2. **Choose the significance level (α):**
- Significance level (α) = 0.10
3. **Calculate the test statistic:**
- We will use the t-test since the sample size (n = 20) is small.
- The test statistic is calculated using the formula:
\[
t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}
\]
Where:
- \(\bar{x}\) = sample mean = 14.6
- \(\mu_0\) = population mean = 14.3
- \(s\) = sample standard deviation = 2.4
- \(n\) = sample size = 20
4. **Determine the critical value:**
- For a two-tailed test at α = 0.10, the critical values for t with (n-1) degrees of freedom (df = 20 - 1 = 19) are approximately ±1.729.
5. **Decision (Critical Value Approach):**
- If the test statistic falls outside the range of -1.729 to 1.729, we reject the null hypothesis.
6. **Decision (p-value Approach):**
- Calculate the p-value associated
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