Question

The Better Business Bureau (BBB) tested the life of 35 diabetes test meters; and found them to last an average of 1450 hours with a standard deviation of 100 hours. The company that produces these meters claims that they last 1500 hours on average. The BBB knows that the population is normally distributed, and traditionally uses a significance level of 5%. Does the BBB have enough evidence to claim that these test meters have a shorter lifespan than the manufacturer claims they do?

Please type in the Critical Value(s) ,

the Test Statistic ,

and the result of the test

Answer 1

H0: >= 1500

Ha: < 1500

Test Criteria :-
Reject null hypothesis if t < -t(α, n-1)
Critical value t(α, n-1) = t(0.05 , 35-1) = -1.691

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 1450 - 1500 ) / ( 100 / √(35) )
t = -2.958

t < - t(α, n-1) = -2.958 < - 1.691
Result :- Reject null hypothesis

We have sufficient evidence to support the claim that these test meters have a shorter lifespan than

the manufacturer claims they do.