Question

A large number of people worldwide take the GMAT exam each year as they apply for MBA programs. Administrators of the test suggest that from past experience the distribution of GMAT exam scores is closely approximated by a normal distribution with mean 1F525 and standard deviation ơ-100 (i)Assuming the population distribution of GMAT exam scores is normal, what is the probability that a person randomly drawn from those taking the test would have a test score between 510 and 550? [1 mark] If an MBA program requires you to get a score that puts you in the top 10% of the distribution, what score is required? [1 mark] (ii) (iii)Testit is a company that sells a coaching service that they claim can improve GMAT exam scores. A regulatory agency that is responsible for overseeing these types of companies wants to examine the claims being made by Testit. Suppose the initial plan is to take a sample of people who have used the services of Testit, the treatment group; and for their GMAT results to be compared to a control group of people who have not used the services of Testit. Do you think this is a good approach to testing the effectiveness of Testit's services? Explain. [3 marks] (iv) Ultimately the approach suggested in (ii) was not undertaken. Instead the regulatory agency recruited a random sample of 100 people who had previously expressed interest in taking the GMAT and then paid for them to go through the Testit training program. With this approach, what would be the null and alternative hypotheses in order to test the claim that the coaching program actually works to improve test scores. If the average test score for this sample is 5404, conduct the test using a significance level of α-0.05 and making clear all necessary assumptions that you make in order to conduct the test. [5 marks] In general, what is the motivation for choosing small significance (α) levels? [1 mark] Again using the sample in (iv), what is the 95% confidence interval for the population mean of GMAT exam scores? Discuss how this confidence interval could be used to test the claims of Testit? Explain why in general this approach of using the confidence interval will not necessarily come to the same conclusion as the approach used in part (iv)? [3 marks] What would be the key features of the distribution of GMAT scores that led administrators of the test to assert that the normal distribution provides a close approximation? What if the administrators of the test were in fact incorrect and the underlying population distribution of test scores was not normal does this impact on your answer in part (iv) in any way? Explain your answer. [4 marks] (v) (vi) (vii)

Answer 1