Reference no: EM132432520

A) a. From the information given here determine the 95% confidence interval estimate of the population mean.

 x bar= 100 σ = 20 n = 25

b. Repeat part (a) with  = 200.

c. Repeat part (a) with  = 500.

d. Describe what happens to the width of the confidence interval estimate when the sample mean increases.

B) a. A random sample of 100 observations was randomly drawn from a population with a standard deviation of 5. The sample mean was calculated as x bar = 400. Estimate the population mean with 99% confidence.

b. Repeat part (a) with  = 200.

c. Repeat part (a) with  = 100.

d. Describe what happens to the width of the confidence interval estimate when the sample mean decreases.

All exercises below assume that the population is normal.

C) Is the sample median an unbiased estimator of the population mean? Explain.

D) Is the sample median a consistent estimator of the population mean? Explain.

E) Show that the sample mean is relatively more efficient than the sample median when estimating the population mean.

F) a. Given the following information, determine the 90% confidence interval estimate of the population mean using the sample median.

Sample median = 500, σ = 12, and n = 50

b. Compare your answer in part (a) to that produced in part (c) of Exercise 10.12. Why is the confidence interval estimate based on the sample median wider than that based on the sample mean?