Question

Grand Auto Corporation produces auto batteries. The company claims that its top-of-theline Never Die batteries are good, on average, for 65 months. A consumer protection agency tested 25 such batteries to check this claim. It found that the mean life of these 25 batteries is 63.4 months. Assume that the life of the batteries follow a normal distribution with standard deviation is 3 months.

(a) Using a 1% significance level, test the hypothesis that the average life of Never Die batteries is less than 65 months.

(b) Construct a 98% confidence interval for the true average life of the Never Die batteries

Answer 1

a)

H0: = 65

Ha:   < 65

Test Statistic :-
t = ( X̅ - µ ) / ( S / √(n))
t = ( 63.4 - 65 ) / ( 3 / √(25) )
t = -2.67
Test Criteria :-
Reject null hypothesis if | t | > t(α/2, n-1)
From T table,
Critical value t(α/2, n-1) = t(0.01 /2, 25-1) = 2.797
| t | > t(α/2, n-1) = 2.67 < 2.797
Result :- Fail to reject null hypothesis

b)

98% Confidence Interval is
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.02 /2, 25- 1 ) = 2.492
63.4 ± 2.492 * 3/√(25)
Lower Limit = 63.4 -2.492 * 3/√(25)
Lower Limit = 61.90
Upper Limit = 63.4 + 2.492 * 3/√(25)
Upper Limit = 64.90
98% Confidence interval is ( 61.90 , 64.90 )