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 mid western town of Webster City showed a sample mean annual consumption of 24.1 gallons with a standard deviation of s = 4.8.

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

H0:
Ha:

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 Selectless than .005between .005 and .01between .01 and .025between .025 and .05between .05 and .10between .10 and .20greater than .20Item 5

What is your conclusion?

Solution

Set Up Hypothesis
Null, H0: U=21.6
Alternate, mean annual consumption in Webster City is higher than the national mean H1: U>21.6
Test Statistic
Population Mean(U)=21.6
Sample X(Mean)=24.1
Standard Deviation(S.D)=4.8
Number (n)=16
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =24.1-21.6/(4.8/Sqrt(15))
to =2.083
| to | =2.083
Critical Value
The Value of |t a| with n-1 = 15 d.f is 1.753
We got |to| =2.083 & | t a | =1.753
Make Decision
Hence Value of | to | > | t a| and Here we Reject Ho
P-Value :Right Tail - Ha : ( P > 2.0833 ) = 0.02737
Hence Value of P0.05 > 0.02737,Here we Reject Ho

ANS:
H0: U=21.6 , H1: U>21.6
to =2.083
between .025 and .05
mean annual consumption in Webster City is higher than the national mean