Question

A car company says that the mean gas mileage for its luxury sedan is at least 22 miles per gallon (mpg). You believe the claim is incorrect and find that a random sample of 6 cars has a mean gas mileage of 19 mpg and a standard deviation of 5 mpg. At alpha equals 0.05, test the company's claim. Assume the population is normally distributed.

A. Which sampling distribution should be used and why?

B. What is the value of the standardized test statistic?

The standardized test statistic is=

C. What is the critical value?

Critical value=

D. What is the outcome and the conclusion of this test?

____Ho. At the 10% significance level, there is _____evidence to ______ the car company's claim that the mean gas mileage for the luxury sedan is at least ….

Answer 1

To Test :-

H0 :-  

H1 :-  

Test Statistic :-


t = -1.4697

Test Criteria :-
Reject null hypothesis if

Critical value =   

Result :- Fail to reject null hypothesis

Decision based on P value
P - value = P ( t > 1.4697 ) = 0.8992
Reject null hypothesis if P value < level of significance
P - value = 0.8992 > 0.05 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

There is sufficient evidence to support the claim that  the claim is incorrect, i.e  the mean gas mileage for its luxury sedan is not at least 22 miles per gallon (mpg)

For  

Test Criteria :-
Reject null hypothesis if


Result :- Fail to reject null hypothesis

Decision based on P value
P - value = P ( t > 1.4697 ) = 0.8992
Reject null hypothesis if P value < level of significance
P - value = 0.8992 > 0.1 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

__Fail to reject __Ho. At the 10% significance level, there is _insufficient____evidence to __accept____ the car company's claim that the mean gas mileage for the luxury sedan is at least ….