Question

Grand Auto Corporation is a manufacturer of automobile batteries. The company claims that its top of the line Never Die batteries are good, on average, for at least 65 months. A consumer protection agency tested a random sample of 36 such batteries to check this claim. It found that sample mean is 63 months. Suppose the population standard deviation is σ = 3 months.

a. At 5% level of significance, can you conclude that the average life of Never Die batteries battery is less than the claimed value? Clearly state your hypotheses, the decision rule, and your decision. Interpret your findings.

b. What is the p-value for this test? What decision would you reach using the p-value approach?

Answer 1

a)

H0: = 65

Ha: < 65

Test statistics

z = - / / sqrt(n)

= 63 - 65 / 3 / sqrt(36)

= -4

This is test statistics value.

Critical value at 0.05 level is -1.645.

Decision rule = Reject H0 if z < -1.645

Since test statistics z falls in rejection region, we have sufficient evidence to reject H0.

We conclude at 0.05 level that we have enough evidence to support the claim.

b)

p-value = P( Z < z)

= P( Z < -4)

= 0

Since p-value < 0.05 significance level, we have sufficient evidence o reject H0.