Problem 2:
An actual outcome can be compared with the probability of getting that outcome by chance alone. This is the basis of inferential statistics. In inferential statistics, we are comparing what we really observe with what would be expected by chance alone. That which would be expected by chance alone would be the null hypothesis (that is, nothing is going on here but chance alone).
If we were to throw a coin, there would be a 50% chance it would come up heads, and a 50% chance it would come up tails by chance alone. By extension, if we threw the coin 20 times, we’d expect 50% (p = .5 or pn = 20*.5 = 10) of the tosses to come up heads, and 50% (q = .5 or qn = 20*.5 = 10) to come up tails by chance alone if this is a fair coin.
a. You aren’t sure if your friend is using a fair coin when he offers to toss the coin to decide who will win $100. You ask him to let you toss the coin 25 times to test it out before you decide whether you will take the bet, using this coin. You toss the coin 25 times and it comes up heads 19 times. Is this a fair coin (the null hypothesis)? What is the probability of getting 19 heads in 25 tosses by chance alone? You have decided that if the outcome of 19/25 tosses as heads would occur less than 5% of the time by chance alone, you will reject the idea that this is a fair coin. (see pp. 184-196 and 699-702 in textbook).
b. Now, suppose the outcome of your trial tosses was 15 heads in 25 tosses. What is the probability of 15 heads in 25 tosses? Would you decide this is a fair coin, using the 5% criterion as in question a (see pp. 184-196 and 699-702 in textbook)?
