Question

The U.S. Dairy Industry wants to estimate the mean yearly milk consumption. A sample of 25 people reveals the mean yearly consumption to be 82 gallons with a standard deviation of 24 gallons. Assume that the population distribution is normal. (Use Distribution Table.) a-1. What is the value of the population mean? 82 24 Unknown a-2. What is the best estimate of this value? Estimate population mean c. For a 90% confidence interval, what is the value of decimal places.) (Round your answer to 3 Value of t d. Develop the 90% confidence interval for the population mean. (Round your answers to 3 decimal places.) and Confidence interval for the population mean is . Would it be reasonable to conclude that the population mean is 75 gallons? Yes O No O It is not possible to tell

T Distribution Table

Answer 1

Solution :

Given that,

a) population mean = unknown

b) Point estimate = sample mean = $\bar x$ = 82

sample standard deviation = s = 24

sample size = n = 25

Degrees of freedom = df = n - 1 = 25 - 1 = 24

c) At 90% confidence level

$\alpha$ = 1 - 90%

$\alpha$ =1 - 0.90 =0.10

$\alpha$/2 = 0.05

t$\alpha$/2,df = t_0.05,24 = 1.711

Margin of error = E = t_{$\alpha$/2,df} * (s /$\sqrt$n)

= 1.711 * ( 24 / $\sqrt$ 25)

Margin of error = E = 8.213

d) The 90% confidence interval estimate of the population mean is,

$\bar x$  ± E

= 82  ± 8.213

= ( 73.787, 90.213 )

e) yes