Question

1. The life in hours of a battery is normally distributed with σ = 1.25 hours. A random sample of 10 batteries has a mean life of 40.6 hours. Is there evidence to support the claim that battery life exceeds 40 hours? Use α = 0.05. You may use the traditional or P-value method.

2. Repeat exercise #1 if we do not know σ, but estimate the population S.D. using s = 1. Use the traditional method.

Answer 1

1)

H0: = 40  

Ha: > 40

Test statistics

z = - / / sqrt(n)

= 40.6 - 40 / 1.25 / sqrt(10)

= 1.52

Critical value at 0.05 level = 1.645

Since test statistics < 1.645, Do not reject H0.

2)

Test statistics

t = - / S / sqrt(n)

= 40.6 - 40 / 1 / sqrt(10)

= 1.90

t critical value at 0.05 level with 9 df = 1.833

Since test statistics value > 1.833, reject H0.