Question

1. A computer company claims that its laptop batteries average more than 4.5 hours of use per charge with a standard deviation of 0.7 hours. A sample of 45 batteries last an average of 4.72 hours. At the .05 level of significance, is there evidence to support the claim that the batteries last more than 4.5 hours?

Answer 1

One sample z test :

Claim : Average battery life more than 4.5 hours

H₀ : µ = 4.5   vs H_a : µ > 4.5  

Given : = 4.72 , σ = 0.7 , n = 45

Population standard deviation σ is known therefore we use z statistic.

Test statistic:

Z =     =

Z = 2.11

Critical value:     α = 0.05

As H_a contain > sign , this is right tail test,

So 1 - α = 0.95 therefore Z_{(1 -α )} = 1.645

Critical region: Reject H₀, if Z ≥ 1.645 Or fail to reject H0 , if Z < 1.645

Decision: As Z is greater than 1.645 , we reject H₀

Conclusion: There is significant evidence that average battery life more than 4.5 hours.