Question

Commute times in the U.S. are heavily skewed to the right. We select a random sample of 45 people from the 2000 U.S. Census who reported a non-zero commute time.

In this sample the mean commute time is 25.2 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

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 30
Alternative Hypothesis, Ha: μ < 30

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (25.2 - 30)/(19.1/sqrt(45))
t = -1.686

P-value Approach
P-value = 0.0494

As P-value < 0.05, reject the null hypothesis.

Sufficient evidence to conclude that the mean commute time in the U.S. is less than half an hour