A Federal funding program is available to low income neighborhoods. To qualify for the funding a neighborhood must have a mean household income of less then $15,000 per year. Neighborhoods with mean household income of $15,000 or more do not qualify. Funding decisions are based on a sample of residents in the neighborhood. A hypothesis test with a .02 level of significance is conducted. If the funding guidelines call for a maximum probability of .05 of not funding neighborhood with a mean annual household income of $14,000, what sample size should be used in the funding decision study? Use sigma = $4000 as a planning value.
mu = $15000
sample mean: <X> = mu - z(alpha)*s/sqrt(n) <= $14000
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