Question

Problem 5:

A bus company advertised a mean time of 150 minutes for a trip between two cities. A consumer group had reason to believe that the mean time was more than 150 minutes. A sample of 20 trips showed a mean x̄ = 153 minutes and a standard deviation s = 7.5 minutes. At an α = .10 level of significance, test the consumer group’s belief. Assume that trip lengths with this bus company follow a normal distribution. Make sure that any necessary assumptions for conducting the hypothesis test are satisfied.

A) State the null and alternative hypothesis.

H₀:

H_a:                                                                                          

B) Determine the critical value(s) for the test.

C) Compute the test statistic (show your work).

D) Make your decision.

E) State your conclusion in terms of the professor’s claim.

                                                           

Answer 1

a)

H0: = 150

Ha: > 150

b)

Critical value t(α, n-1) = t(0.1 , 20-1) = 1.328

c)

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 153 - 150 ) / ( 7.5 / √(20) )
t = 1.79

d)

Test Criteria :-
Reject null hypothesis if t > t(α, n-1)

t > t(α, n-1) = 1.7889 > 1.328
Result :- Reject null hypothesis

e)

We have sufficient evidence to conclude that the true mean time was more than 150 minutes.