Before approval is given for the use of a new insecticide th

Before approval is given for the use of a new insecticide, the United States Department of Agriculture requires that several tests be performed to see how the substance will affect wildlife. In particular, the USDA would like to know the proportion of starlings that will die after being exposed to the insecticide. A random sample of 80 starlings were caught and fed their regular food, which had been treated with the substance. After 10 days, 10 startlings had died. Use a 96% confidence interval to estimate the true proportion of starlings that will be killed by the new insecticide. Interpret your confidence interval in the context of the problem. *College graduate statistical methods problem*

Solution

Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=10
Sample Size(n)=80
Sample proportion = x/n =0.125
Confidence Interval = [ 0.125 ±Z a/2 ( Sqrt ( 0.125*0.875) /80)]
= [ 0.125 - 2.05* Sqrt(0.0014) , 0.125 + 2.05* Sqrt(0.0014) ]
= [ 0.0492,0.2008]