Question

1. LSAT is an exam that university students take if they are interested in applying to med school. A professor said, "Because only a minority of university students take the LSAT, the scores overestimate the ability of a typical university student. The mean LSAT score is about 508, but I think that if all the students took the test, the mean score would be no more than 450".

This professor gave the test to a random sample of 500 students in Ontario and found that these students had a mean score of x = 461.

1. Is this good evidence against the claim that the mean for all students is no more than 450? For this example, let us assume that the population standard deviation σ of MCAT scores in our Ontario population is 100. Please give me rational analysis and reasoning with both calculation and interpretation
2. Would this statistically significant result be significant in a practical sense? Please describe what the statistically significant result mean and write a paragraph explaining the reasoning.

Answer 1

(a) The hypothesis being tested is:

H0: µ 450

Ha: µ > 450

x = 461

σ = 100

n = 500

z = (x - µ)/σ/√n

z = (461 - 450)/100/√500

z = 2.46

The p-value is 0.0070.

Since the p-value (0.0070) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we cannot conclude that the mean for all students is no more than 450.

(b) In principle, a statistically significant result (usually a difference) is a result that’s not attributed to chance. More technically, it means that if the Null Hypothesis is true (which means there really is no difference), there’s a low probability of getting a result that large or larger.