**Hypothesis Testing: Evaluating the Effectiveness of a Review Course**A math teacher claims that she has developed a review course that increases the scores of students on the math portion of a college entrance exam. Based on data from the administrator of the exam, scores are normally distributed with a population mean (μ) of 524. The teacher obtains a random sample of 2000 students, puts them through the review class, and finds that the mean math score of the 2000 students is 532 with a standard deviation of 117. Complete parts (a) through (d) below.### (a) State the null and alternative hypotheses:- Null Hypothesis (H₀): μ = 524- Alternative Hypothesis (H₁): μ > 524### (b) Test the hypothesis at the α = 0.10 level of significance. Is a mean math score of 532 statistically significantly higher than 524? Conduct a hypothesis test using the P-value approach.- Find the test statistic (t₀): \[ t₀ = \] (Round to two decimal places as needed.)### Explanation of Process:1. **Null and Alternative Hypotheses:** - **H₀:** μ = 524 (The mean score after the review course is equal to the general mean score). - **H₁:** μ > 524 (The mean score after the review course is greater than the general mean score, indicating the course is effective).2. **Level of Significance:** - α = 0.10, which represents a 10% risk of concluding that a difference exists when there is no actual difference.3. **Test Statistic:** - Calculated using the formula for the test statistic in hypothesis testing for the mean with a known standard deviation: \[ t₀ = \frac{\bar{x} - \mu}{\left(\frac{\sigma}{\sqrt{n}}\right)} \] where: - \( \bar{x} \) is the sample mean (532), - \( \mu \) is the population mean (524), - \( \sigma \) is the population standard deviation (117), - \( n \) is the sample size (2000).Given the sample mean (532), population mean (524), population standard deviation (117), and sample size (2000), calculate

Given that n=2000x¯=532s=117α=0.10

Answered: A math teacher claims that she has…

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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