Question

The U.S. Dairy Industry wants to estimate the mean yearly milk consumption. A sample of 21 people reveals the mean yearly consumption to be 74 gallons with a standard deviation of 16 gallons. Assume that the population distribution is normal. (Use t Distribution Table.)

a-1.	What is the value of the population mean?
	16 Unknown 74

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

Estimate population mean

c.	For a 90% confidence interval, what is the value of t? (Round your answer to 3 decimal places.)

Value of t

d.	Develop the 90% confidence interval for the population mean. (Round your answers to 3 decimal places.)

Confidence interval for the population mean is  and .

e.	Would it be reasonable to conclude that the population mean is 68 gallons?
	It is not possible to tell. Yes No

Answer 1

Given:

Sample mean = x bar = 74 , sample standard deviation s = 16 , n = 21 , C = 0.90

a-1) Here population mean is not given.

Hence value of population mean is Unknown.

a-2) We know that sample mean is best estimate of population mean. Hence

Estimate of population mean = 74

c) For 90% confidence interval we get-

By using t table and degrees of freedom = n - 1 = 20

t_(0.90,20) = 1.725

d) 90 % confidence interval is :

e) Here 68 falls in the above interval hence it is reasonable to conclude that population mean is 68 gallons.

Hence YES

Hope this will help you. Thank you :)