Question: A modification has been made to the production line which produces a certain electronic component. Past evidence shows that lifetimes of the components have a population standard deviation of 700 hours. It is believed that the modification will not affect the population standard deviation, but may affect the mean lifetime. The previous mean lifetime was 3250 hours. A random sample of 50 components made with the modification is taken and the sample mean lifetime for these components is found to be 3575 hours. Should the manufacturer conclude that the new process produces components with longer mean lifetimes?

a) Compute the probability of finding a sample mean component lifetime of 3575 hours or more in a random sample of 50 components. Use this probability to answer the manufacturer’s question.

b) An alternative approach is to compute a 95% confidence interval for the true mean lifetime. Compute such an interval using the same information above. Use this confidence interval to answer the manufacturer’s question.

c) Test your statistical writing skills. Write a clear, concise, and accurate interpretation of the confidence interval in part b).