Question

An investigator in the Statistics Department of a large university is interested in the effect of exercise in maintaining mental ability. She decides to study the faculty members aged 40 to 50 at his university, looking separately at two groups: The ones that exercise regularly, and the ones that don’t. There turn out to be several hundred people in each group, so she takes simple random sample of 25 persons from each group, for detailed study. One of the things she does is to administer an IQ test to the sample people, with the following results: Regular Exercise No Regular Exercise Sample size 25 25 Average score 130 120 Standard deviation 15 15 The investigator concludes that exercise does indeed help to maintain mental ability among the faculty members aged 40 to 50 at his university. Is this conclusion justified? Explain whether you agree with her and show your reasoning mathematically. (20 points)

Answer 1

Let group1 (x1): Regular excercise

Group 2 (x2): no regular excercise

Here we need to right tailed test.

Conclusion: Since we reject the null hypothesis so we can conclude that conclusion justified.