Question

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 were selected, and each one drove a car from Phoenix to Los Angeles. The resulting fuel efficiencies (in miles per gallon) are given below.

27.1

29.2

31.3

28.4

30.2

29.6

Assuming that fuel efficiency is normally distributed under these circumstances, do the data contradict the claim that true average fuel efficiency is (at least) 30 mpg? Test the appropriate hypotheses at significance level 0.05. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.)

t=

P-value=

Answer 1

For the given data sample mean is

Create the following table.

data	data-mean	(data - mean)2
27.1	-2.2	4.84
29.2	-0.1	0.01
31.3	2	4
28.4	-0.9	0.81
30.2	0.9	0.81
29.6	0.3	0.09

Find the sum of numbers in the last column to get.

So standard deviation is

Here hypothesis is vs

Hence test statistics is

As it is left tailed test P value is TDIST(1.18,5,1)=0.146