The owner of Brittens Egg Farm wants to estimate the mean nu

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

A.
Population mean is unknown
Point of estimate = 20
B.
Population standadrd deviation is unknown, we use t distribution in such case
C.
it is 2.093
D.
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=20
Standard deviation( sd )=2
Sample Size(n)=20
Confidence Interval = [ 20 ± t a/2 ( 2/ Sqrt ( 20) ) ]
= [ 20 - 2.093 * (0.447) , 20 + 2.093 * (0.447) ]
= [ 19.064,20.936 ]
E.
21 is n\'t . It is out of bound from the interval calculated in D
25 is n\'t . It is out of bound from the interval calculated in D