Coffee for breakfast in the 1960\'s was a commonplace method of becoming more al

Question

Coffee for breakfast in the 1960's was a commonplace method of becoming more alert for classes among college students. However, coffee makers have seen a decline in U.S. coffee consumption and are obviously concerned about it. One coffee maker decides to estimate the proportion of college students (likely candidates for coffee) who drink coffee for breakfast nationally. The proportion of the total population who drink coffee for breakfast is about 0.55. The coffee maker decides to use 0.55 as the value for p in determining the sample size to select from among college students. A 92% confidence interval is chosen and the estimate, p, is to be within 0.05 of the true proportion of college students who drink coffee for breakfast. Compute the needed sample size. n =

Explanation / Answer

Let sample size be n

proportion mean estimator = 0.57

1-alpha = 92%

alpha = 0.08

alpha/2 = 0.16

1-alpha/2 = 0.84

z = 0.994458 from Normal Table

Let sample size be n

standard deviation estimator = sqrt{p*(1-p)/n} = sqrt(0.57*0.43/n)

Error = z*sqrt{p*(1-p)/n} <= 0.04

sqrt{p*(1-p)/n} <= 0.04/z = 0.04/0.994458 = 0.040223

p*(1-p)/n <= 0.001618

n>= 0.57*0.43/0.001618 = 151.4942

n = 152

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