Question 977663
In both cases, the margin of error is E = 0.04. The critical value is approximately z = 1.96 (found using a table or calculator)



A)


"no preliminary estimate is available" so assume that p = 0.5


n = p(1-p)(z/E)^2


n = 0.5(1-0.5)(1.96/0.04)^2


n = 600.25


n = 601


Notice how I rounded up to the nearest whole number.


Min sample size needed is 601


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b)


Now we are told that p = 0.48


n = p(1-p)(z/E)^2


n = 0.48(1-0.48)(1.96/0.04)^2


n = 599.2896


n = 600


Again, round up to the nearest integer.


Min sample size needed is 600


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There isn't much difference between the two min sample sizes: 601 from part a) and 600 from part b)