Question

Commute times in the U.S. are heavily skewed to the right. We select a random sample of 200 people from the 2000 U.S. Census who reported a non-zero commute time. In this sample the mean commute time is 27.5 minutes with a standard deviation of 18.9 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?  

Answer 1

Given : Sample size=n=200

Sample mean= minutes

Sample standard deviation=s=18.9 minutes

Significance level=

Hypothesized value= minutes

Hypothesis : Vs  

The test statistic is ,

d.f.=degrees of freedom=n-1=200-1=199

The p-value is ,

p-value=

The Excel function for p-value , =TDIST(1.8707,199,1)

Decision : Here , p-value=0.031<

Therefore , reject Ho.

Conclusion : Hence , the data provide the sufficient evidence to support the claim that the mean commute time in the U.S. is less than half an hour.