Question

Annual per capita consumption of milk is 21.6 gallons (Statistical Abstract of the United States: 2006). Being from the Midwest, you believe milk consumption is higherthere and wish to support your opinion. A sample of 16 individuals from the Midwestern town of Webster City showed a sample mean annual consumption of 24.1 gallonswith a sample standard deviations = 4.8.

a. Develop a hypothesis test that can be used to determine whether the mean annual consumption in Webster City is higher than the national mean.

b. What is a point estimate of the difference between mean annual consumption in Webster City and the national mean?

c. At a=.05, test for a significant difference. What is your conclusion?

Answer 1

The test hypothesis is
Ho:μ=21.6
Ha:μ>21.6

The test statistic is

t=(xbar-μ)/(s/√n)

=(24.1-21.6)/(4.8/4)

= 2.08

Given a=0.05, the critical value is |t(0.05, df=n-1=15)|=1.75 (check student t table)

Since t=2.08 is larger than 1.75, we reject Ho.