Question

A study found that the average stopping distance of a school bus traveling 50 miles per hour 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 miles per hour was 262.3 feet. The standard deviation was 3 feet. To test the claim that the average stopping distance of the company’s buses is actually less than 264 feet,

State the hypotheses, Calculate the Test Statistic, find the P-Value, and make the decision whether to reject Ho or not, using α= 0.05.

Answer 1

H0: = 264

Ha: < 264

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 262.3 - 264 ) / ( 3 / √(20) )
t = -2.53

From T table,

With test statistics of 2.53 and df of 19,

p-value = 0.0102

Since p-value < 0.05, Reject H0

We conclude that we have sufficient evidence to support the claim that the average stopping  

distance of the company’s buses is actually less than 264 feet.