Question

The Zambezi car battery manufacturer claims that the average lifespan of batteries produced by his firm is at least 30 months. The rival manufacture the Rehoboth batteries disagree and took random sample of 100 Zambezi car batteries and recorded a mean of 31.7 months and a standard deviation of 8 months. (Show all your works) Determine the following: a) The null and alternative hypotheses 3 b) The test statistic value. 5 c) The critical statistics value at 99% confidence level 5 Page 11 of 13 d) The rejection region using critical value approach 2 e) The p value at 99% confidence level 5 f) The rejection region using both the p value approach 2 g) Make conclusion about the population mean using both approaches

Answer 1

To Test :-
H0 :- µ < 30
H1 :- µ >= 30

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 31.7 - 30 ) / ( 8 / √(100) )
t = 2.125

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

Critical Value t(α, n-1) = t(0.01 , 100-1) = 2.365

t > t(α, n-1) = 2.125 < 2.365
Result :- Fail to reject null hypothesis

Decision based on P value
P - value = P ( t > 2.125 ) = 0.018
Reject null hypothesis if P value < α = 0.01 level of significance
P - value = 0.018 > 0.01 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

There is insufficient evidence to support the claims that the average lifespan of batteries produced by his firm is at least 30 months.