A statistics practitioner took a random sample of 50

Question

Econ 310, Spring 2014- Week 9:

Problem 1- Let X¯ and Y¯ be two unbiased, consistent estimators for µ_X and µ_Y, respectively.

1. Show that X¯ - Y¯ is an unbiased estimator for µ_X - µ_Y.

2. Show that X¯ - Y¯ is a consistent estimator for µ_X - µ_Y.

Problem 2- Which estimator for µ_X is more efficient: X1(the first observation) or X¯?

Problem 3- A statistics practitioner took a random sample of 50 observations from a population whose standard deviation is 25 and computed the sample mean to be 100. (Hint: z_0.1 = 1.28, z_0.05 = 1.645, z_0.025 = 1.96, z_0.005 = 2.575).

1. Estimate the population mean with 90% confidence level.

2. Repeat 1 with 95% confidence level.

3. Repeat 1 with 99% confidence level.

4. Describe the effect on the confidence interval estimate of increasing the confidence level.

Problem 4- The operations manager of a plant making cellular telephones has proposed rearranging the production process to be more efficient. She wants to estimate the time to assemble the telephone using the new arrangement. She believes that the population standard deviation is 15 seconds. How large a sample of workers should she take to estimate the mean assembly time to within 2 seconds with 95% confidence?