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 laid per chicken. A sample of 20 chickens shows they laid an average of 19 eggs per month with a standard deviation of 5 eggs per month. (a-1) What is the value of the population mean? 5 19 It is unknown. (a-2) What is the best estimate of this value? Best estimate (c) For a 90% confidence interval, what is the value of t? (Round your answer to 3 decimal places.) Value of t (d) Determine the 90% confidence interval for the population mean. is (Round your answers to 2 decimal places.) Confidence interval to (e-1) Would it be reasonable to conclude that the population mean is 25 eggs? No Yes (e-2) What about 21 eggs? No Yes

Solution

sample size,n = 15
sample mean,xbar = 22
standard deviation,s = 7

a.
population mean is unknown.

b.
best estimate of this value = xbar = 22

c.
alpha,a = 1-0.90 = 0.1
critical value = t(a/2,n-1)
= t(0.05, 14)
= 1.761

d.
confidence interval:
xbar +/- [t(a/2,n-1) * (s/sqrt(n))]
22 +/- [1.761 * (7/sqrt(15))]
22 +/- 3.18
= ( 18.82 , 25.18 )

e.
Since both 26 and 28 lies outside the confidence interval so
e-1
NO
e-2
NO