AboutJason Eisele Expertise I am qualified to answer probability questions through the undergraduate level. I can also assist with the first actuarial exam in probability and explain the roles of probability in applications such as economics and game theory.
I hope to address any topics that I am currently unfamiliar with during my studies as an actuary.
Experience I am beginning employment as an Actuarial Assistant with a major auto insurer. On the side, I have experience applying probability to poker at a highly competitive level.
Organizations Mensa
Education/Credentials University of Rochester Class of 2008:
Bachelor of Arts, Mathematics and Economics
Certificate in Actuarial Studies
Certificate in Mathematical Modeling in Political Science and Economics
Certificate in Management Studies with track in Accounting and Finance
Question i'm currently taking applied math right now and my background in math is pretty shallow. can you help me solve this problem?
A teacher claims in his particular metaphysics class that each student can write a 30 page essay. A random sample of 28 students revealed that the average written pages was 27. the standard deviation of the sample was 18, at the .05 level of significance, can we conclude that more than 30 pages are made on the average by a student.
Answer Hi Dominic,
Thank you for your question!
We can never conclude that a true mean is above (or below) the sample mean by sampling alone. What confidence intervals help us do is determine a range (centered on the sample mean) of possible true means with a high degree of confidence--they cannot conclude any diversion from the sample mean because our sample mean is our best estimator.
Even though the teacher claims his students can write 30 pages, this claim provides absolutely no evidence. That is why we analyze the claim with statistics.
It is handy to remember that .05 level of significance can allow for possible true means up to two standard deviation away from the sample mean when the distribution we are analyzing is approximately normal. Two standard deviation in this case is 36, so we can say with 95% certainty that the true mean lies between 0 (because it can't possibly be lower and 63 (=27+36).
So it is possible that the true mean is above 30, but remember that our confidence interval must always contain the sample mean. Despite any claims, we can never prove that the sample mean is not the true mean. When you read the question again, do you think that arriving at a sample mean of 27 proves the teacher's claim?
With more study, this will develop your intuition with regards to confidence intervals. Thanks again!
