The owner of Britten’s Egg Farm wants to estimate the mean number of eggs produc

Question

The owner of Britten’s Egg Farm wants to estimate the mean number of eggs produced per chicken. A sample of 19 chickens shows they produced an average of 21 eggs per month with a standard deviation of 7 eggs per month. (Use t Distribution Table.)
a-1. What is the value of the population mean? 21, It is unknown, OR 7
a-2. What is the best estimate of this value?
c. For a 95% confidence interval, what is the value of t? (Round your answer to 3 decimal places.)
d. Develop the 95% confidence interval for the population mean. (Round your answers to 2 decimal places.)
e-1. Would it be reasonable to conclude that the population mean is 17 eggs? No or Yes
e-2. What about 24 eggs? No or Yes

Explanation / Answer

A-1)It is unknown

A-2)  best estimate of this value =21

c) for (n-1=18) degree of freedom and 95% CI ; t =2.101

d) for std error of mean =std deviation/(n)1/2 =7/(19)1/2 =1.606

therefore 95% confidence inteval =sample mean -/+ t*std error =17.63 ; 24.37

e-1) as 17 falls outside our confidence interval values; it is not reasonable ; No

e-2) as 24 falls inside  our confidence interval values; it is reasonable ; Yes

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