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) Conduct a hypothesis test with significance level of 0.05 to answer the manufacturer’s question, using the p-value approach.

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.

Note: you can use approximate formula (with Z value) or exact formula (with t value) c) Which of the following is an accurate interpretation of the confidence interval in part b)? ______

A. There is a 95% chance that true mean lies in the interval we calculated.

B. We are 95% confident that our interval contains the true mean.

Answer 1

(c) Option: A. There is a 95% chance that true mean lies in the interval we calculated.