Question

A study found that the average stopping distance of a school bus traveling 50 mph was 264 feet. A group of automotive engineers decided to conduct a study of its school buses and found that for 20 buses, the average stopping distance of buses traveling 50 mph was 262.3 feet. The standard devia- tion of the population was 3 feet. Test the claim that the average stopping distance of the company’s buses is actually less than 264 feet. Find the P-value. On the basis of the P-value, should the null hypothesis be rejected at α = .05. Assume the variable is normally distributed.

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :   = 264

H_a : < 264

Test statistic = t

= ( - ) / s / n

= (262.3 - 264) / 3 / 20

= -2.53

Test statistic = -2.53

n = 20

df = 20 - 1 = 19

P-value = 0.9898

= 0.05  

P-value >

Fail to reject the null hypothesis .

There is not sufficient evidence to that the average stopping distance of the company’s buses is actually less than 264 feet