Question

The life in hours of a battery is known to be normally distributed with ?=1.25 hours. A random sample of 10 batteries has a mean life of ?̅=30.5 hours. Is there evidence to support the claim that battery life exceeds 32 hours? Is the alternative hypothesis one or two sided? Do you reject the null hypothesis? Use ?=0.05

Answer 1

Solution,

The null and alternative hypothesis is ,

H0 :   = 32

Ha : > 32

= 30.5

= 1.25

n = 10

This is one tailed test,

Test statistic = z =

= ( - ) / / n

= (30.5 - 32) / 1.25 / 10

Test statistic = z = -3.79

P(Z < -3.79)

P-value = 0.0001

= 0.05  

P-value <

Reject the null hypothesis .