Corn: In a prior sample of corn, farmer Carl finds that 16% of the sample has wo
ID: 3149903 • Letter: C
Question
Corn: In a prior sample of corn, farmer Carl finds that 16% of the sample has worms but the margin of error for his population estimate was too large. He wants an estimate that is in error by no more than 2.5 percentage points at the 95% confidence level. Enter your answers as whole numbers. (a) What is the minimum sample size required to obtain this type of accuracy? Use his prior sample proportion in your calculation. (b) What is the minimum sample size required to obtain this type of accuracy when you assume no prior knowledge of the sample proportion?
Explanation / Answer
a)
Note that
n = z(alpha/2)^2 p (1 - p) / E^2
where
alpha/2 = 0.025
Using a table/technology,
z(alpha/2) = 1.959963985
Also,
E = 0.025
p = 0.16
Thus,
n = 826.0673048
Rounding up,
n = 827 [ANSWER]
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b)
Note that
n = z(alpha/2)^2 p (1 - p) / E^2
where
alpha/2 = 0.025
As there is no previous estimate for p, we set p = 0.5.
Using a table/technology,
z(alpha/2) = 1.959963985
Also,
E = 0.025
p = 0.5
Thus,
n = 1536.583528
Rounding up,
n = 1537 [ANSWER]