The owner of the Brittens Egg Farm wants to estimate the mea

The owner of the Britten\'s Egg Farm wants to estimate the mean number of eggs produced per chicken.  A representative random sample of 20 chickens show they produce an average of 25 eggs per month with a sample standard deviation (s) of 2 eggs per month. The distribution is known to be symmetrical and is close enough to normal to be treated as a normal distribution.

Answer the following questions related to and calculate a 90% confidence interval for the mean number of eggs produced per chicken on the Britten\'s Egg Farm.

What is the point estimate of the mean number of eggs produced per chicken?

Enter answer with 0 decimal places (integer).

What is the appropriate distribution for calculating a 90% confidence interval?

a     Uniform distribution

b     Normal distribution

c     t distribution

d     Chi Square distribution

Answer this question by entering the appropriate letter.

What is the degrees of freedom (dF) for this problem. Enter Na if dF is not required by the applicable distribution.

Calculate the margin of error for the 90% confidence interval for the mean amount of eggs laid per month on the Britten\'s Egg Farm.

Enter answer rounded to 1 decimal point. Include a zero to the left of the decimal point if the margin of error is a number between -1 and +1.

The 90% conference interval for the mean number eggs produced per month is:

Enter the lower and upper limits for the conference interval by entering the lower limit first.
Rounded each conference limit to 1 decimal point.

Prior to this study the owner of the Britten\'s Egg Farm Egg Farm believed the mean amount off eggs produced per month on his farm was 30.

Does the study support his belief with a 90% confidence?

a     Yes. The mean amount of eggs produced per month on his farm could be 30 per month because the number 30 is not contained in the confidence interval.

b     Yes. The mean amount of eggs produced per month on his farm could be 30 per month because the number 30 is contained in the confidence interval.

c     No. The mean amount of eggs produced per month on his farm is most likely not 30 per month because the number 30 is not contained in the confidence interval.

d     No. The owner can not comment on the mean amount of eggs produced per month on his farm because the confidence interval is based upon a sample.

Enter the correct answer by selecting and entering the appropriate letter.

Solution

What is the point estimate of the mean number of eggs produced per chicken?

25

What is the appropriate distribution for calculating a 90% confidence interval?

b     Normal distribution

What is the degrees of freedom (dF) for this problem

NA

Calculate the margin of error for the 90% confidence interval for the mean amount of eggs laid per month on the Britten\'s Egg Farm.

alpha = 1 - 0.90 =0.10

alpha/2 = 0.05

Z = 1.64

error = 1.64 * 2 / srqt(20)

error = 0.7334 = 0.7

The 90% conference interval for the mean number eggs produced per month is:

I : 25 +/- 0.7

I : 24.3 , 25.7

c     No. The mean amount of eggs produced per month on his farm is most likely not 30 per month because the number 30 is not contained in the confidence interval.