Question: In the movie “When Harry Met Sally”, there is a scene where Meg Ryan is shopping for a Christmas tree. The film shows a beautiful snowy night in New York city and Meg Ryan dragging her tree back to her apartment. Suppose the mean height of a sample of n=15 Christmas trees was \[\bar{X}\] = 143 cm. Assume that the population of tree heights is normal with known standard deviation σ =18 cm.

a. (5 points) Construct a 90% confidence interval estimate of the unknown mean μ.

b. (5 points) Have a look at the CI that you constructed in answering question #1a. On the basis of its lower bound, is it reasonable to say that the average tree height in the population is at least 130 cm? Explain.