Question

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.

Answer 1

1. The significance level of my test is _____%.
2. The power of my test is _____%.

Answer 2

the standard deviation would appear to be sqrt(npq): sqrt(10000*.49*.51), or about 49.99

Answer 3

but then that doesnt help out much ....

\[\Large Z =\frac{H_a-H_o}{\sqrt{\frac{\mu H_o(1-\mu H_o)}{n}}}\]
\[\frac{.505-.49}{\sqrt{\frac{.49~.51}{10000}}}=3.0006...\]
so if ive done this correctly, thats like a 99% CI

Answer 4

or, since 50/100 = .5 .. try that with a .50 instead of the .505 maybe?

Answer 5

which if ive done it correctly leads to a cutoff of 2.00004 ... which is about a 95% CI

Answer 6

@amistre64 The null is 49%. So z = -0.025. and then?

Answer 7

the cutoff is at 5000 out of 10000; so .50 is the test statistic for this; and we have a one tailed test