Question

Researchers are planning a study to estimate the impact on crop yield when no-till is used in combination with residue retention and crop rotation. Based on data from a meta-analysis of 610 small farms, the researchers estimate there is a 2.5% decline in crop yield when no-til is used with residue retention and crop rotation. Suppose the researchers want to produce a 90% confidence interval with a margin of error of no more than 7.0%. Determine the minimum sample size required for this study. The sample size needed to create a confidence interval estimate depends on the margin of error, the initial estimated proportion, and the confidence level. Be sure to use proportions rather than percentages. Round your final answer up to the nearest whole number. n=_____________________held comparisons

Answer 1

Answer: n= 14

Step-by-step explanation:

The formula to find the sample size :_

$n= p(1-p)(\dfrac{z^*}{E})^2$

, where p= Prior estimate of population proportion.

z* =  Critical value.

E= Margin of error.

Given : Prior estimate of population proportion : p= 0.025

We know that  , the critical value for 90% confidence interval :

$z^*=1.645$

E= 7.0%=0.070

Then , the required minimum sample size :

$n= (0.025)(1-0.025)(\dfrac{1.645}{0.07})^2\\\\=(0.025)(0.975)(23.5)^2\\\\13.46109375\approx14$

i.e. n= 14

Hence, the sample size needed : n= 14