MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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**Educational Content: Understanding Hypothesis Testing**

**Scenario:**
A math teacher claims to have developed a review course that improves student scores on the math portion of a college entrance exam. The exam scores are normally distributed with a mean (μ) of 525. A random sample of 2200 students who took the course had a mean score of 530 with a standard deviation of 119. 

**Task: Test the Hypotheses in Parts a to d**

**Response Options:**
- **C.** Yes, because every increase in score is practically significant.
- **D.** No, because the score became only 0.95% greater.

**Part D: Hypothesis Test at α = 0.10 Level**

1. **Calculate the Test Statistic (t₀):**
   - Use the sample size (n = 400), sample mean (530), population mean (525), and sample standard deviation (119).
   - Formula: \( t₀ = \frac{\text{Sample Mean} - \text{Population Mean}}{\text{Standard Deviation}/\sqrt{n}} \)
   - Round to two decimal places.

2. **Find the P-value:**
   - Based on the test statistic, determine the P-value.
   - Round to three decimal places.

3. **Determine Statistical Significance:**
   - Is the sample mean of 530 statistically significantly higher than 525?

   Options:
   - **A.** No, because the P-value is greater than α = 0.10.
   - **B.** No, because the P-value is less than α = 0.10.
   - **C.** Yes, because the P-value is greater than α = 0.10.
   - **D.** Yes, because the P-value is less than α = 0.10.

4. **Impact of Large Samples on P-Values:**
   - How does the size of the sample affect the likelihood of rejecting the null hypothesis?

   Options:
   - **A.** As \( n \) increases, the likelihood of rejecting the null hypothesis increases. However, large samples may overemphasize practically insignificant differences.
   - **B.** As \( n \) increases, the likelihood of not rejecting the null hypothesis increases. Large samples tend to overemphasize practically insignificant differences.
   - **C.** As \( n \)
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Transcribed Image Text:**Educational Content: Understanding Hypothesis Testing** **Scenario:** A math teacher claims to have developed a review course that improves student scores on the math portion of a college entrance exam. The exam scores are normally distributed with a mean (μ) of 525. A random sample of 2200 students who took the course had a mean score of 530 with a standard deviation of 119. **Task: Test the Hypotheses in Parts a to d** **Response Options:** - **C.** Yes, because every increase in score is practically significant. - **D.** No, because the score became only 0.95% greater. **Part D: Hypothesis Test at α = 0.10 Level** 1. **Calculate the Test Statistic (t₀):** - Use the sample size (n = 400), sample mean (530), population mean (525), and sample standard deviation (119). - Formula: \( t₀ = \frac{\text{Sample Mean} - \text{Population Mean}}{\text{Standard Deviation}/\sqrt{n}} \) - Round to two decimal places. 2. **Find the P-value:** - Based on the test statistic, determine the P-value. - Round to three decimal places. 3. **Determine Statistical Significance:** - Is the sample mean of 530 statistically significantly higher than 525? Options: - **A.** No, because the P-value is greater than α = 0.10. - **B.** No, because the P-value is less than α = 0.10. - **C.** Yes, because the P-value is greater than α = 0.10. - **D.** Yes, because the P-value is less than α = 0.10. 4. **Impact of Large Samples on P-Values:** - How does the size of the sample affect the likelihood of rejecting the null hypothesis? Options: - **A.** As \( n \) increases, the likelihood of rejecting the null hypothesis increases. However, large samples may overemphasize practically insignificant differences. - **B.** As \( n \) increases, the likelihood of not rejecting the null hypothesis increases. Large samples tend to overemphasize practically insignificant differences. - **C.** As \( n \)
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