Question

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 95% confidence level. Enter your answers as whole numbers, What is the minimum sample size required to obtain this type of accuracy?

Answer 1

Answer: 741

Step-by-step explanation:

As per given ,we have

The prior estimate of population proportion: $p=0.14$

Margin or error : 2.5%=0.025

Critical value for 95% confidence = $z_{\alpha/2}=1.96$

Formula to find the sample size :-

$n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2$

i.e. $n=0.14(1-0.14)(\dfrac{1.96}{0.025})^2$

$=740.045824\approx741$

Hence, the minimum sample size required to obtain this type of accuracy= 741