Question

Suppose a sample of 16 light trucks is randomly selected off the assembly line. The trucks are driven 1000 miles and the fuel mileage (MPG) of each truck is recorded. It is found that the mean MPG is 22 with a SD equal to 3. The previous model of the light truck got 20 MPG.

Questions:

a) State the null hypothesis for the problem above

b) Conduct a test of the null hypothesis at p = .05. BE SURE TO PROPERLY STATE YOUR STATISTICAL CONCLUSION.

c) Provide an interpretation of your statistical conclusion using the variables from the description given

Answer 1

Given that,
population mean(u)=20
standard deviation, σ =3
sample mean, x =22
number (n)=16
null, Ho: μ=20
alternate, H1: μ!=20
level of significance, α = 0.05
from standard normal table, two tailed z α/2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 22-20/(3/sqrt(16)
zo = 2.667
| zo | = 2.667
critical value
the value of |z α| at los 5% is 1.96
we got |zo| =2.667 & | z α | = 1.96
make decision
hence value of | zo | > | z α| and here we reject Ho
p-value : two tailed ( double the one tail ) - ha : ( p != 2.667 ) = 0.008
hence value of p0.05 > 0.008, here we reject Ho
ANSWERS
---------------
a.
null, Ho: μ=20
alternate, H1: μ!=20
b.
test statistic: 2.667
critical value: -1.96 , 1.96
decision: reject Ho
p-value: 0.008
c.
we have enough evidence to support the claim that The previous model of the light truck got 20 MPG.