Question

Corn: In a prior sample of corn, farmer Carl finds that 12% 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.

The minimum sample size is  ears of corn.

(b) What is the minimum sample size required to obtain this type of accuracy when you assume no prior knowledge of the sample proportion?

The minimum sample size is  ears of corn.

Answer 1

Given that, estimate of the proportion = p = 0.12

margin of error (E) = 2.5% = 0.025

A 95% confidence level has significance level of 0.05 and critical value is,

We want to find, the sample sizes for the following cases :

a) If we use a prior sample proportion = 0.12, then sample size is,

Therefore, the minimum sample size is 649 ears of corn.

Note : if you want sample size is to next whole number then n = 650

b) If we don't use the prior sample proportion then sample size is,

Therefore, the minimum sample size is 1537 ears of corn.