Question

The U.S. Dairy Industry wants to estimate the mean yearly milk consumption. A sample of 14 people reveals the mean yearly consumption to be 60 gallons with a standard deviation of 20 gallons. Assume the population distribution is normal. (Use t Distribution Table.)

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

• 20

• 60

• Unknown

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

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

4. Develop the 95% confidence interval for the population mean. (Round your answers to 3 decimal places.)

5. Would it be reasonable to conclude that the population mean is 52 gallons?

• Yes

• No

• It is not possible to tell.

Answer 1

Given that, sample size (n) = 14

sample mean = 60 gallons and

sample standard deviation = 20 gallons

a-1) The value of the population mean is unknown

a-2) The best estimate of the population mean is sample mean = 60 gallons

c) Degrees of freedom = 14 - 1 = 13

t-critical value at significance level of 0.05 with 13 degrees of freedom is,

=> t-critical value = 2.160

d) The 95% confidence interval for the population mean is,

Therefore, required confidence interval is, (48.454, 71.546).

e) Given that, population mean = 52

Since, 52 is lies in above interval, it is reasonable to conclude that the population mean is 52 gallons.

Answer : Yes