help lol A math teacher claims that she has developed a review course that increases scores of students on the math portion of a college entrance exam. Based on data from the College Board, scores are normallydistributed with u=511. 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 of114. Complete parts (a) through (d) below.Click the icon to view the t-Distribution Area in the Right Tail.(a) State the null and alternative hypotheses.Но(b) Test the hypothesis at the a=0.10 level of significance. Is a mean math score of 518 statistically significantly higher than 511? Conduct a hypothesis test using the P-value approach.Find the test statistic.H₁16=0(Round to two decimal places as needed.)Approximate the P-value corresponding to the critical value of t.The P-value isIs the sample mean statistically significantly higher?O A. No, ause the P-value range is above a=0.10.OB. Yes, because the P-value range is above a=0.10.OC. No, because the P-value range is below a=0.10.O D. Yes, because the P-value range s below a=0.10.fel Do you think that a moan math croro nf 518 vorcuc 511 will affort the doricion of a school admiccione administrator? In other worde dooc the incroace in the crora hava anu nractical cinnificanca?Submit quiz7:58 PM12/4/2022 the Right Tallto = U(Round to two decimal places as needed.)Approximate the P-value corresponding to the critical value of t.The P-value isIs the sample mean statistically significantly higher?4OA. Yes, because the P-value range is above α=0.10.OB. No, because the P-value range is below a=0.10.OC. Yes, because the P-value range is below a=0.10.OD. No, because the P-value range is above α = 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 significant 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 insignificant differences.

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Accepted Answer

It is given that 
Population mean = 511
Sample mean, M = 518
Standard deviation = 114
Sample size =…