The owner of Britten\'s Egg Farm wants to estimate the mean number of eggs laid

Question

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

Explanation / Answer

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

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