Question

A company with a large fleet of cars hopes to keep gasoline costs down and sets a goal of attaining a fleet average of at least 27 miles per gallon. To see if the goal is being met, they check the gasoline usage for 50 company trips chosen at random, finding a mean of 26.07 mpg and a standard deviation of 5.24 mpg. Is this strong evidence they have failed to attain their fuel economy goal? Complete parts a through e below.

a) Write appropriate hypotheses. b) Are the necessary assumptions to perform inference satisfied? c) Test the hypothesis and find the P-value. d) Explain what the P-value means in this context. e) State an appropriate conclusion.

Answer 1

Solution

a.)

H₀:μ> 27

H_a : μ<27

b.)samples are randomly selected that is first condition is satisfied, population standard deviation is unknown and sample size(n)=50, so this can be assume the normal distribution.

Hence, All condition are satisfied.

c.)now,

n=50, x̅=26.07, μ=27, s=5.24

as population standard deviation is unknown so we will go for t test

Test Statistic:

t=(x̅-μ)/(s/sqrt(n)

=(26.07-27)/(5.24/sqrt(50))

=-1.25

P-value=P(t₄₉>-1.25)=1-P(t₄₉<-1.25)=1-0.1086=0.8914

Here we took defaule value of significance (α)=0.05

so here, P-value>significance, we failed to reject Null hypothesis.

e)

The average gasoline usage of the fleet of cars is at least 27 miles per gallon.