Question

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 90% 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

90% confidence interval means = 0.10 level of significance

Error by no more than 2.5% means E = 0.025

a)

Minimum sample size,

n = 457.2 ~458

b)

Here

assume no prior knowledge of the sample proportion

So we can take

So,

= 1082.41 ~ 1083