Question

A highway construction zone has a posted speed limit of 40 miles per hour. Workers working at the site claim that the mean speed of the vehicles passing through this constuction zone is at least 50 miles per hour. You think the workers claim is wrong and want to prove it. A random sample of 36 vehicles passing through this zone produced a mean speed of 48 miles per hour. The population standard deviation is known to be 4 miles per hour. Test the hypothesis that the workers claim is wrong, and that the average speed is less than 50mph using a 2.5% significance level.

Answer 1

This is the left tailed test .

The null alternative hypothesis is

H₀ : = 50

H_a : < 50

Test statistic = z

= ( - ) /    / n

= (48 - 50) / 4 / 36

Test statistic = -3

P-value = 0.0013

P-value <

Reject the null hypothesis .

There is sufficient evidence to conclude that the average speed is less than

50 mph using a 2.5% significance level.