The owner of Britten’s Egg Farm wants to estimate the mean number of eggs produced per chicken. A sample of 20 chickens shows they produced an average of 20 eggs per month with a standard deviation of 2 eggs per month.
a. What is the value of the population mean? What is the best estimate of this value?
b. Explain why we need to use the t distribution. What assumption do you need to make?
c. For a 95% confidence interval, what is the value of t?
d. Develop the 95% confidence interval for the population mean.
e. Would it be reasonable to conclude that the population mean is 21 eggs? What about 25 eggs?
Solution:
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