Question

The owner of Britten's Egg Farm wants to estimate the mean number of eggs laid per chicken. A sample of 36 chickens shows they laid an average of 28 eggs per month with a standard deviation of 15 eggs per month.  

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

(Click to select)  It is unknown.  28.00  15

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

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

(Click to select)  We must assume that the population is not normally distributed.  We must assume that the population is binomially distributed.  We must assume that the population is 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 32 eggs?

(Click to select)  Yes  No

What about 36 eggs?

(Click to select)  Yes  No

Answer 1

a-1) The population mean is unknown.

a-2) The point estimate of mean is = 28

b-1) Use the t-distribution as the population standard deviation is unknown.

b-2) We must assume that the population is normally distributed.

c) At 80% confidence level, the critical value is t^* = 1.306

d) The 80% confidence interval is

e) No, since 32 does not lie in the confidence interval.

No, since 36 does not lie in the confidence interval.