Question

The owner of Britten's Egg Farm wants to estimate the mean number of eggs laid per chicken. A sample of 34 chickens shows they laid an average of 27 eggs per month with a standard deviation of 14 eggs per month.  

a-1. What is the value of the population mean?

(Click to select)  It is unknown.  27.00  14

a-2. What is the best estimate of this value?

b-1. Explain why we need to use the t distribution.

(Click to select)  Use the t distribution as the population standard deviation is known.  Use the t distribution as the population mean is known.  Use the t distribution as the population standard deviation is unknown.

b-2. What assumption do you need to make?

(Click to select)  We must assume that the population is binomially distributed.  We must assume that the population is normally distributed.  We must assume that the population is not normally distributed.

c. For a 80% confidence interval, what is the value of t? (Round the final answer to 3 decimal places.)

The value of t is  .

  

d. Develop the 80% confidence interval for the population mean. (Round the final answers to 2 decimal places.)

The 80% confidence interval for the population mean is  to  .

e. Would it be reasonable to conclude that the population mean is 31 eggs?

(Click to select)  Yes  No

What about 35 eggs

Answer 1

Solution:

a -1)

What is the value of the population mean?

It is unknown.

a-2. What is the best estimate of this value?

27

b-1. Explain why we need to use the t distribution.

Use the t distribution as the population standard deviation is unknown.

b-2. What assumption do you need to make?

We must assume that the population is normally distributed.

c. For a 80% confidence interval, what is the value of t?

Here , c = 80% = 0.80

= 1- c = 1- 0.00 = 0.20

  /2 = 0.20 2 = 0.10

n = 34

df = n - 1 = 34 - 1 = 33

    =    =  _{0.10 , 33} = 1.308

Answer : 1.308

( use t table or t calculator to find this value..)

d. Develop the 80% confidence interval for the population mean.

The margin of error is given by

E =  /2,d.f. * ( / n)

= 1.308 * (14 / 34)

= 3.140

Now , confidence interval for mean() is given by:

( - E ) <   <  ( + E)

(27 - 3.140)   <   <  (27 + 3.140)

23.860 <   < 30.140

Required 80% confidence interval is (23.860 , 30.140)

e. Would it be reasonable to conclude that the population mean is 31 eggs?

No , because 31 is not in the interval.