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In: Statistics and Probability

Question 2: Many dairy farms have experienced bankruptcy over the past decade as a result of...

Question 2:
Many dairy farms have experienced bankruptcy over the past decade as a result of wild
fluctuation in conventional milk prices. However, organic farms, those that do not treat
cows with antibiotics or hormones and use only hay grown without chemicals, have remained
solvent and expanded. In a random sample of 1400 New England dairy farms, 90 are certified
as organic.


a. Find a 88.58% confidence interval for the true proportion of the organic farms in New
England.


b. If we use this study as a pilot study and plan to conduct a new study, we wish to control
the interval length of the 88.58% interval to be at most 0.02. How many farms need
to be included in the sample? (Use the part (a) result in the sample size calculation.)


c. Perform a test with Ha : p > 0.10, at 0.05 level. Report the p-value.

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