Problem 7 A manufacturer of automobile batteries claims that the distribution of
ID: 3051702 • Letter: P
Question
Problem 7 A manufacturer of automobile batteries claims that the distribution of lengths of life of its batteries has a mean of 54 months and a standard deviation of 6 months. Suppose a consumer group decides to check the claim by purchasing a sample of 49 of these batteries and subjecting them to tests that determine battery life. (a) Describe the sampling distribution of the mean lifetime of a sample of 49 batteries. (b) What is the probability that consumer group's sample has a mean life of 52 or fewer months? (c) Based on the answer to part (b), does the consumer group have a strong evidence that the manufacture's claim is untrue?Explanation / Answer
Solution:- Given that mean = 54, sd = 6 , n = 49
a) mean of the sample means = 54
std of sample means = 6/sqrt(54) = 0.8165
b) P(x-bar < 52) = P(Z < (x - mu)/(sd/(sqrt(n)))
= P(Z < (52 - 54)/(0.8165)
= P(Z < -2.4494)
= 0.0071
c) If the manufacturer's claim were true, the probability of obtaining a value as small as or smaller than 52 is .0071. Assuming a 5% level of significance this probability is too small.
Hence, his claim cannot be rejected