28 Oct Assuming a significance level
For the purposes of this problem, assume the roulette has 52 numbers, 26 red and 26 green (there are no 0s). You want to create an experiment where you get to watch the roulette N times, and observe the numbers that it picks (from 1–52, red and green). Your null hypothesis is that the roulette is “fair,” i.e. it picks green and red numbers with equal probability. The alternative hypothesis is that it is not fair, and it picks red with a probability of p = 0.50 + δ, where δ is a small number (positive or negative, note that under the null δ = 0). Assuming a significance level of 1%, how large does N have to be to have a test with power of 90% against the alternative that δ = 0.005? Assuming a significance level of 1%, how large does N have to be to have a test with power of 90% against the alternative that δ = 0.002?
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