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In: Statistics and Probability

Suppose that GMAT scores of all MBA students in Canada are normally distributed with a mean...

Suppose that GMAT scores of all MBA students in Canada are normally distributed with a mean of 550 and a standard deviation of 120.

a. A university (that is representative of the MBA students in the U.S.) claims that the average GMAT scores of students in its MBA program are at least 550. You take a sample of 121 students in the university and find their mean GMAT score is 530. Can you still support the University’s claim? Test at 5% significance level. Interpret the test result.

b. Calculate the p-value for the test in part (a). If the hypothesis was to be tested at 10% significance level instead of 5% would your answer to part (a) change? Explain why without actually conducting the test.

c.Do you need the assumption that “GMAT scores of all MBA students in the U.S. are normally distributed” to answer part (a) or (b)? Explain.

d. You discover that the population standard deviation you’ve been using is actually the sample standard deviation. All other sample information holds. If you were still conducting the hypothesis test as you set up in part (a), would your test statistic/ distribution change? How?

And would you need the assumption of normality of the population now? Why?

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Expert Solution

orchestra answered 2 years ago
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