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?

Your answer should be rounded to 4 decimal places.

Answer 1

Solution :

$\mu$= 30

$\bar x$ =27.5

$\sigma$ =18.9

n = 200

This is the less tailed test .

The null and alternative hypothesis is ,

H₀ :  $\mu$ = 30

H_a : $\mu$ < 30

Test statistic = z

= ($\bar x$ - $\mu$ ) / $\sigma$ / $\sqrt$ n

= (27.5-30) / 18.9/ $\sqrt$ 200

= -1.87

P(z <-1.87 ) = 0.0307

P-value = 0.0307

$\alpha$ = 0.05  

P-value < $\alpha$

Reject the null hypothesis .