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 sample standard deviation of 2.91 eggs per month.

(a-1)	What is the value of the population mean?
	(Click to select)2.9119It is unknown.
(a-2)	What is the best estimate of this value?

(c)	For a 95 percent confidence interval, the value of t is . (Round your answer to 3 decimal places.)

(d)	The 95 percent confidence interval for the population mean is  to  (Round your answers to 3 decimal places.)

(e-1)	Would it be reasonable to conclude that the population mean is 22 eggs?
	(Click to select)YesNo
(e-2)	What about 24 eggs?
	(Click to select)YesNo

Answer 1

The provided sample mean is 19 and the sample standard deviation is s=2.91. The size of the sample is n = 20 and the required confidence level is 95%.

The number of degrees of freedom are df = 20 - 1 = 19 , and the significance level is α=0.05.

Based on the provided information, the critical t-value for α=0.05 and df = 19 degrees of freedom is t_c = 2.093

The 95% confidence for the population mean μ is computed using the following expression

Therefore, based on the information provided, the 95 % confidence for the population mean μ is

CI = (17.638, 20.362)

What is the value of the population mean?

It is unknown.We can only estimate it.

What is the best estimate of this value?

Sample mean = 19 is the best estimate

For a 95 percent confidence interval, the value of t is . (Round your answer to 3 decimal places.)

t = 2.093

The 95 percent confidence interval for the population mean is  to  (Round your answers to 3 decimal places.)

CI = (17.638, 20.362)

Would it be reasonable to conclude that the population mean is 22 eggs?

No, since the interval do not have 22

Would it be reasonable to conclude that the population mean is 24 eggs?

No, since the interval do not have 24