Consumers own laptops of brand X for a certain amount of time before buying a new model. This time duration has a distribution with unknown mean and standard deviation 1.5. The company X expects that consumers will keep their laptop or 3.5 years. After collecting a sample of 27 customers they calculate a sample mean of 4 years. Is there enough evidence (95% significance) to support the claim that laptops are kept for more than 3.5 years?

Question

Consumers own laptops of brand X for a certain amount of time before buying a new model. This time duration has a distribution with unknown mean and standard deviation 1.5. The company X expects that consumers will keep their laptop or 3.5 years. After collecting a sample of 27 customers they calculate a sample mean of 4 years. Is there enough evidence (95% significance) to support the claim that laptops are kept for more than 3.5 years?

Answer 1

Z = (score-mean)/SEm = (4-3.5)/SEm

SEm = SD/√n

Look in the back of your statistics textbook for a table called something like “area under normal distribution” to find the proportion/probability related to the Z score.