How to determine the width of the zone of acceptance in hypothesis testing?

amberglo
Messages
5
Reaction score
0
First and foremost, I am terrible in Stats so bear w/ me on this one. This is my question, if anyone has an idea on how to figure out this problem that would be great! Here it is: Suppose you flip a coin 100 times and you want to test the hypothesis that the coin is fair, making sure there is less than a 5 percent chance of erroneously rejecting the fair coin hypothesis. How wide should the zone of acceptance be? How wide should the zone be if you flip the coin 5 times?
 
Physics news on Phys.org
What you want is a range balanced around the mean which has cumulative probability 95%. The chance of 2 or 3 heads out of 5 flips is
((5 choose 2) + (5 choose 3)) / 2^5 = 20/32
The chance of 1 to 4 heads is
((5 choose 1) + (5 choose 2) + (5 choose 3) + (5 choose 4)) / 2^5 = 30/32

With 100 flips, you are probably intended to use the normal curve as an approximation rather than the explicit binomial formula, although either would work.
 
Namaste & G'day Postulate: A strongly-knit team wins on average over a less knit one Fundamentals: - Two teams face off with 4 players each - A polo team consists of players that each have assigned to them a measure of their ability (called a "Handicap" - 10 is highest, -2 lowest) I attempted to measure close-knitness of a team in terms of standard deviation (SD) of handicaps of the players. Failure: It turns out that, more often than, a team with a higher SD wins. In my language, that...
Hi all, I've been a roulette player for more than 10 years (although I took time off here and there) and it's only now that I'm trying to understand the physics of the game. Basically my strategy in roulette is to divide the wheel roughly into two halves (let's call them A and B). My theory is that in roulette there will invariably be variance. In other words, if A comes up 5 times in a row, B will be due to come up soon. However I have been proven wrong many times, and I have seen some...
Back
Top