# statistics

posted by
**Jimmy Fallon** on
.

There are two boxes, each with several million tickets marked “1” or “0”. The two boxes have the same number of tickets, but in one of the boxes, 49% of the tickets are marked “1” and in the other box 50.5% of the tickets are marked “1”. Someone hands me one of the boxes but doesn’t tell me which box it is.

Consider the following hypotheses:

Null: p = 0.49 Alternative: p = 0.505

Here is my proposed test: I will draw a simple random sample of 10,000 tickets, and if 5,000 or more of them are marked “1” then I will choose the alternative; otherwise I will stay with the null.

The significance level of my test is _____%. [Please be careful to enter your answer as a percent; that is, if your answer is 50% then please enter 50 in the blank; not 50%, nor 0.5, nor 1/2, etc.]

The power of my test is _____%. [Please be careful to enter your answer as a percent; that is, if your answer is 50% then please enter 50 in the blank; not 50%, nor 0.5, nor 1/2, etc.]