Many dairy farms have experienced bankruptcy over the past decade due to the wil

Question

Many dairy farms have experienced bankruptcy over the past decade due to the wild fluctuations in conventional milk prices. However, organic farms, those that do not treat cows with antibiotics or hormones and that use feed grown without chemicals, have remained solvent and even expanded. In a random sample of 1400 New England dairy farms, 90 are certified as organic. Fill in the blanks. (Give your answers to four decimal places.)

A 99% confidence interval for the true proportion of New England dairy farms certified as organic is (, ).

Explanation / Answer

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)=90
Sample Size(n)=400
Sample proportion = x/n =0.225
Confidence Interval = [ 0.225 ±Z a/2 ( Sqrt ( 0.225*0.775) /400)]
= [ 0.225 - 2.576* Sqrt(0.0004) , 0.225 + 2.58* Sqrt(0.0004) ]
= [ 0.1712,0.2788]

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