Question

The manufacturer of a certain electronic component claims that they are designed to last just slightly more than 4 years
because they believe that customers typically replace their device before then. Based on information provided by the
company, the components should last a mean of 4.24 years with a standard deviation of 0.45 years. For this scenario,
assume the lifespans of this component follow a normal distribution

A journalist believes that, in reality, these components have a shorter lifespan than what the company is reporting. He tests a random group of 35 of these components and finds a mean lifespan of 4.05 years.

a. What is the mean of the sampling distribution of sample means when 35 random components are tested?

b. What is the standard error of the sampling distribution when 35 random components are tested?

c. If the company’s reported lifespan distribution were really true, what is the probability that a random group of 35 will have a sample mean lifespan of 4.05 years or less?

d. Would this be a significant result? A. Yes B. No C. Not enough information

Answer 1

a. What is the mean of the sampling distribution of sample means when 35 random components are tested?

4.05 years

b. What is the standard error of the sampling distribution when 35 random components are tested?

0.45/35 = 0.0761

c. If the company’s reported lifespan distribution were really true, what is the probability that a random group of 35 will have a sample mean lifespan of 4.05 years or less?

z = (x - µ)/σ/√n

z = (4.05 - 4.24)/0.45/√35 = -2.50

The probability is 0.0062.

d. Would this be a significant result? A. Yes