Question

Commute times in the U.S. are heavily skewed to the right. We select a random sample of 510 people from the 2000 U.S. Census who reported a non-zero commute time.

In this sample, the mean commute time is 28.0 minutes with a standard deviation of 19.1 minutes. Can we conclude from this data that the mean commute time in the U.S. is less than half an hour? Conduct a hypothesis test at the 5% level of significance.

What is the p-value for this hypothesis test?

(Your answer should be rounded to 4 decimal places.)

Answer 1

To Test :-

H0 :- µ >= 0.30
H1 :- µ < 0.30

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 28 - 30 ) / ( 19.1 / √(510) )
t = -2.3647

Decision based on P value
P - value = P ( t > 2.3647 ) = 0.0092
Reject null hypothesis if P value < α = 0.05 level of significance
P - value = 0.0092 < 0.05 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

There is sufficient evidence to support the claim that  the mean commute time in the U.S. is less than half an hour.