Help with Stats Question?

Question

My teacher asked us a very odd Stats question please help !..

How would I figure this out?:


For the following problems:
1. State the Null Hypothesis and the Alternative Hypothesis
2. Determine the test statistic.
3. Determine the P-value
4. Make a decision regarding the hypotheses based on the P-value and the Level of
Significance.

8. In a recent year, some professional baseball players complained that umpires were calling more strikes than the average rate of 61% called the previous year. At one point in the season, umpire Dan Morrison called strikes in 2231 of 3581 pitches (based on data from USA Today). Use a 0.05 significance level to test the claim that his strike rate is greater than 61%.

Answer 1

This is NOT an odd question; it strikes to the heart of the major use of statistics - making decisions on the basis of uncertain data.

Here, there are two possibilities, Dan Morrison is calling strikes at essentially the same rate as they were last year or he is calling strikes at a significantly higher rate. What does the data suggest?

Consider a coin with probability of heads = the probability of tails = 1/2

Suppose you toss such a coin twice. On "average", you'd expect one heads and one tails. Does getting two heads in a row mean the coin is not fair? No - the probability of two heads in a row is 1/4. Just how many heads in a row would it take to convince you that the coin is bad? Keeping in mind that even a good coin will have 7 heads in a row about one time in 100.

More generally, out of 1000 coin tosses you'd expect approximately 500 heads and 500 tails, but the chances of getting exactly 500 and 500 isn't all that great. Just how far from a 50-50 split would the results have to be to convince you that the coin is biased?

This question is leading you through the thinking process for a similar problem. Each outcome still has only two possibilities (strike vs. not), but now, in a minor complication, the odds are not 50-50 but 61-39. And instead of 1000 outcomes, you are asked to use all the data you have: 3581 outcomes.

And, to make things easier, you are also told just how unlikely the result has to be before you decide it doesn't fit. You are told that if the odds of calling 2231 strikes out of 3581 pitches is less than 0.05 (19-1) with last year's strike calling rate, then that isn't his calling rate this year.