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 u = 512. 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 518 with a standard deviation of 115. Complete parts (a) through (d) below. (a) State the null and alternative hypotheses. Ho : VOH,: VVO (b) Test the hypothesis at the o = 0.10 level of significance. Is a mean math score of 518 statistically significantly higher than 512? Conduct a hypothesis test using the P-value approach. Find the test statistic. to = 0 (Round to two decimal places as needed.) Find the P-value. The P-value is (Round to three decimal places as needed.) Is the sample mean statistically significantly higher? O A. No, because the P-value is greater than a = 0.10. O B. Yes, because the P-value is less than a = 0.10. O C. Yes, because the P-value is greater than a = 0.10. O D. No, because the P-value is less than a = 0. 10. (c) Do you think that a mean math score of 518 versus 512 will affect the decision of a school admissions administrator? In other words, does the increase in the score have any practical significance? O A. Yes, because the score became more than 1.17% greater. O B. Yes, because every increase in score is practically significant. O C. No, because the score became only 1.17% greater. O D. No, because every increase in score is practically significant. (d) Test the hypothesis at the a = 0.10 level of significance with n = 400 students. Assume that the sample mean is still 518 and the sample standard deviation is still 115. Is a sample mean of 518 significantly more than 512? Conduct a hypothesis test using the P-value approach. Find the test statistic. to = 0 (Round to two decimal places as needed.)(d) Test the hypothesis at the a = 0. 10 level of significance with n = 400 students. Assume that the sample mean is still 518 and the sample standard deviation is still 115. Is a sample mean of 518 significantly more than 512? Conduct a hypothesis test using the P-value approach. Find the test statistic. to = 0 (Round to two decimal places as needed.) Find the P-value. The P-value is (Round to three decimal places as needed.) 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. O C. Yes, because the P-value is greater than a = 0.10. O D. 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. O B. As n increases, the likelihood of not rejecting the null hypothesis increases. However, large samples tend to overemphasize practically significant differences. O C. As n increases, the likelihood of not rejecting the null hypothesis increases. However, large samples tend to overemphasize practically insignificant differences. O D. As n increases, the likelihood of rejecting the null hypothesis increases. However, large samples tend to overemphasize practically significant differences