Question

A manufacture of car batteries claims its new batteries will have a mean lifetime of 4 years. A random sample of 35 batteries found the mean lifetime to be 3.91 years. If the population standard deviation is known to be 0.22 years; is there enough evidence, at the 0.05 significance level, to suggest the mean lifetime is less than 4 years?.

Answer 1

Solution :

This is the left tailed test,  

The null and alternative hypothesis is ,

H0 :   = 4

Ha : < 4

Test statistic = z

= ( - ) / / n

= (3.91- 4) / 0.22 / 35

Test statistic = z = -2.42

P(Z < -2.42)

P-value = 0.0078

= 0.05  

P-value <

Reject the null hypothesis .

There is sufficient evidence to suggest that the mean lifetime is less than 4 years