Question

Commute times in the U.S. are heavily skewed to the right. We select a random sample of 500 people from the 2000 U.S. Census who reported a non-zero commute time.

In this sample, the mean commute time is 28.4 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?

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

Answer 1

Here claim is that mean is less than half an hour.

So hypothesis is vs

As sample size is sufficient large we will use z statistics

As test is left tailed P value is

As P value is less than alpha, we reject the null hypothesis. Hence we have sufficient evidence to support the claim that mean is less than than half an hour