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 datafrom the administrator of the exam, scores are normally distributed with µ = 510. The teacher obtains a random sample of 2200 students, puts them through thereview class, and finds that the mean math score of the 2200 students is 515 with a standard deviation of 113. Complete parts (a) through (d) below.(b) Test the hypothesis at the o = 0.10 level of significance. Is a mean math score of 515 statistically significantly higher than 510? Conduct a hypothesis test usingthe P-value approach.Find the test statistic.to =0%3D(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?A. Yes, because the P-value is less than a = 0.10.B. Yes, because the P-value is greater than a = 0.10.C. No, because the P-value is less than a = 0.10.D. No, because the P-value is greater than a = 0.10.(c) Do you think that a mean math score of 515 versus 510 will affect the decision of a school admissions administrator? In other words, does the increase in thescore have any practical significance?A. No, because every increase in score is practically significant.B. Yes, because every increase in score is practically significant.C. Yes, because the score became more than 0.98% greater.D. No, because the score became only 0.98% greater.(d) Test the hypothesis at the a = 0.10 level of significance with n = 350 students. Assume that the sample mean is still 515 and the sample standard deviation is still113. Is a sample mean of 515 significantly more than 510? Conduct a hypothesis test using the P-value approach.Find the test statistic.to(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?A. No, because the P-value is less than a = 0.10.B. Yes, because the P-value is less than x = 0.10.OC. No, because the P-value is greater than a = 0.10.D. Yes, because the P-value is greater 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 significant differences.B. As n increases, the likelihood of not rejecting the null hypothesis increases. However, large samples tend to overemphasize practically insignificantdifferences.C. As n increases, the likelihood of rejecting the null hypothesis increases. However, large samples tend to overemphasize practically insignificant differences.D. As n increases, the likelihood of not rejecting the null hypothesis increases. However, large samples tend to overemphasize practically significantdifferences.O OO O

“Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

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 = 510. 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 515 with a standard deviation of 113. Complete parts (a) through (d) below. (b) Test the hypothesis at the a= 0.10 level of significance. Is a mean math score of 515 statistically significantly higher than 510? 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. Yes, because the P-value is less than a = 0.10. O B. Yes, because the P-value is greater than a = 0.10. OC. No, because the P-value is less than a = 0.10. D. No, because the P-value is greater than a = 0.10. (c) Do you think that a mean math score of 515 versus 510 will affect the decision of a school admissions administrator? In other words, does the increase in the score have any practical significance? O A. No, because every increase in score is practically significant. O B. Yes, because every increase in score is practically significant. O C. Yes, because the score became more than 0.98% greater. O D. No, because the score became only 0.98% greater. (d) Test the hypothesis at the a= 0.10 level of significance with n= 350 students. Assume that the sample mean is still 515 and the sample standard deviation is still 113. Is a sample mean of 515 significantly more than 510? Conduct a hypothesis test using the P-value approach. Find the test statistic. to = (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 less than a= 0.10. O B. Yes, because the P-value is less than a = 0.10. O C. No, because the P-value is greater than a = 0.10. O D. Yes, because the P-value is greater 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 significant differences. O B. As n increases, the likelihood of not rejecting the null hypothesis increases. However, large samples tend to overemphasize practically insignificant differences. O C. As n increases, the likelihood of rejecting the null hypothesis increases. However, large samples tend to overemphasize practically insignificant differences. O D. As n increases, the likelihood of not rejecting the null hypothesis increases. However, large samples tend to overemphasize practically significant differences.