Question

A manufacturer of car batteries advertises that the average life of their batteries is 54 months. A consumer “watchdog” group selects a random sample of 100 batteries to test the manufacturer’s claim. The consumer group is suspicious that the batteries do not last as long as the claim. The sample mean is 52 months. Assume a known population standard deviation (sigma) of 6 months.

A. Write out Ho and Ha.

B. Using MegaStat, calculate the p-value and provide MegaStat output for documentation.

C. Can we reject Ho at the 95% confidence level? Can we be 95% confident that the manufacturer’s claim is false? CAREFULLY EXPLAIN WHY OR WHY NOT.

Answer 1

Ans:

a)

b)

Test statistic:

z=(52-54)/(6/sqrt(100))

z=-3.333

p-value=P(z<-3.333)=0.0004

critical z value=-1.645

(reject H0,if z<-1.645)

c)As,p-value<0.05,we reject the null hypothesis.

There is sufficient evidence to reject the manufacturer’s claim.(i.e. we can conclude that the manufacturer’s claim is false)