Annual per capita consumption of milk is 216 gallons Statist

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 higher there 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 23.4 gallons with a standard deviation s = 4.5.

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

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

At  = .05, test for a significant difference by completing the following.

Calculate the value of the test statistic (to 2 decimals).

The p-value is

Solution

We have given that

Annual per capita consumption of milk is 21.6 gallons

Being from the Midwest, you believe milk consumption is higher there 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 23.4 gallons with a standard deviation s = 4.5.

Here the hypothesis for the test is,

H0 : µ = 21.6 Vs H1 : µ > 21.6

Here sample information is given so we use t-test here.

Also the test is one sided and right tailed.

alpha = level of significance = 0.05

The test statistic is,

t = (Xbar - µ) / s/sqrt(n)

Xbar is sample mean = 23.4

s is standard deviation of sample = 4.5

n is sample size = 16

t = (23.4 - 21.6) / [ 4.5/sqrt(16) ] = 1.6

The  point estimate of the difference between mean annual consumption in Webster City and the national mean is 1.8

test statistic = 1.6

p-value =

p-value we can calculate by using EXCEL.

syntax : =tdist(x , d.f.,tails)

x is the test statistic value

d.f. = n - 1 = 16 - 1 = 15

tails = 1

p-value = 0.065

p-value > alpha(0.05)

fail to reject H0 at 5% level of significance.

Annual per capita consumption of milk is 21.6 gallons