**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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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 distribuléd with ji525 The teacher obtains a random sample of 2200 students, puts them through the review class, and finds that the mean math score of the 2200 students is 530 with a standard deviation of 119. Complete parts (a) through (d) below. O C. Yes, because every increase in score practically significant. O D. No, because the score became only 0.95% greater. (d) Test the hypothesis at the a = 0.10 level of significance with n=400 students. Assume that the sample mean is still 530 and the sample standard deviation is still 119. Is a sample mean of 530 significantly more than 525? Conduct a hypothesis test using the P-value approach. Find the test statistic. (Round to two decimal places as needed.) Find the P-value. The P-value is. (Round to three decimal places as needed.) Question Viewer Is the sample mean statistically significantly higher? O A. No, because the P-value is greater than a = 0.10. O B. No, because the P-value is less than a=0.10. OC. Yes, because the P-value is greater than a = 0.10. OD. Yes, because the P-value is less than a =0.10. What do you conclude about the impact of large samples on the P-value? O A. As n increases, the likelihood of rejecting the null hypothesis increases. However, large samples tend to overemphasize practically insignificant differences. OB. As n increases, the likelihood of not rejecting the null hypothesis increases. However, large samples tend to overemphasize practically insignificant differences. OC. As n increases, the likelihood of rejecting the null hypothesis increases. However, large samples tend to overemphasize practically significant differences. O D. As n increases, the likelihood of not rejecting the null hypothesis increases. However, large samples tend to overemphasize practically significant differences.