Question

Corn: In a prior sample of corn, farmer Carl finds that 14% 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

Solution :

Given that,

(a)

= 1 - = 0.5

margin of error = E = 0.025

Z/2 = 1.645

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.645 / 0.025)2 * 0.5 * 0.5

= 1082

The minimum sample size is 1082 ears of corn.

(b)

= 0.14

1 - = 1 - 0.14 = 0.86

margin of error = E = 0.025

Z/2 = 1.645

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.645 / 0.025)2 * 0.14 * 0.86

= 521

The minimum sample size is 521 ears of corn