The average annual miles driven per vehicle in the United St

The average annual miles driven per vehicle in the United States is 11.1 thousand miles, with 600 miles. Suppose that a random sample of 41 vehicles owned by residents of Chicago showed that the average mileage driven last year was 10.9 thousand miles. Does this indicate that the average miles driven per vehicle in Chicago is different from (higher or lower than) the national average? Use a 0.05 level of significance.

What is the value of the sample test statistic? (Round your answer to two decimal places.)

Find the P-value. (Round your answer to four decimal places.)

Solution

Set Up Hypothesis
Null Hypothesis H0: U=11.1
Alternate, average miles in Chicago is different from national average H1: U!=11.1
Test Statistic
Population Mean(U)=11.1
Given That X(Mean)=10.9
Standard Deviation(S.D)=0.6
Number (n)=41
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=10.9-11.1/(0.6/Sqrt(41)
Zo =-2.1344
| Zo | =2.1344
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =2.1344 & | Z | =1.96
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Two Tailed ( double the one tail ) - Ha : ( P != -2.1344 ) = 0.0328
Hence Value of P0.05 > 0.0328, Here we Reject Ho

We don\'t have evidence to conclude average miles driven per vehicle in Chicago is different from (higher or lower than) the national average