An automobile manufacturer who wishes to advertise that one of
its models achieves 30 mpg (miles per gallon) decides to carry out
a fuel efficiency test. Six nonprofessional drivers are selected
from the entire population, and each one drives a car from Phoenix
to Los Angeles. The resulting fuel efficiencies (in miles per
gallon) are 24.9, 28.7, 36.3, 25.7, 30.5, 31.8. Assuming that fuel
efficiency is normally distributed under these circumstances, do
the data contradict the claim that the mean fuel efficiency of the
population is (at least) 30 mpg? Perform a relevant hypothesis test
for the research question using α = 0.05. Follow the steps
given below: Step#1: Set up a null hypothesis H0 and an alternative
hypothesis Ha about the research question. Step#2: Compute the
t-test statistic of the sample. Show your work. Step#3: Show your
decision on H0 based on the p-value at α = 0.05. Show your work.
(Note: Round to the nearest thousandth as needed.)