Question

The u.s. dairy industry wants to estimate the mean yearly milk consumption. a sample of 16 people reveals the mean yearly consumption to be 60 gallons with a standard deviation of 20 gallons. (a-1) what is the value of the population mean? 20 unknown 60 (a-2) what is the best estimate of this value? estimated 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 63 gallons? yes it is not possible to tell. no

Answer 1

1-2. The best estimate for the population mean would be sample mean of 60 gallons. Since we know that the sample mean is the best point of estimate. Since sample size n=16 is less than 25, we use the t distribution. Assume population from normal distribution.

3. Given a=0.1, the t (0.05, df = n – 1 = 15)=1.75

4. xbar ± t*s/vn = 60 ± 1.75*20/4 = ( 51.25, 68.75)

5. Since the interval include 63, it is reasonable.