Econometrics - Hypothesis testing.
How many people should you survey? You want to take a random sample of likely voters in order to estimate the proportion (p) of voters in that population who prefer candidate A over candidate B. You need to decide how large a sample you should take.
(a) It’s expensive to survey many people, so in your first try you just go ahead and take a modest sample of size 40. In this sample, 25 people support A. Based on this sample, compute a 95% confidence interval for p. Can you reject, at 5% significance, that the candidates have equal support (p = 0.5)?
(b) Suppose that, in fact, p = 0.51 (that’s in the population, not in your sample). How large will your sample size n need to be in order to detect such a departure from 0.50 (equal support) with 5% significance (i.e. give you enough power to detect a difference of 0.01)?