# AMBA 600 Problem Set 2 Updated

**AMBA 600 Problem Set 2 Updated**

Probability

1. Suppose that the mean of the annual return for common stocks from 2000 to 2012 was 14.37%, and the standard deviation of the annual return was 35.14%. Suppose also that during the same 12-year time span, the mean of the annual return for long-term government bonds was 0.6%, and the standard deviation was 2.1%. The distributions of annual returns for both common stocks and long-term government bonds are bell-shaped and approximately symmetric in this Assume that these distributions are distributed as normal random variables with the means and standard deviations given previously.

Find the probability that the return for common stocks will be greater than 16.32%.

Find the probability that the return for common stocks will be greater than 5.89%.

Find the probability that the return for common stocks will be less than 14.37%.

Hint: There are many ways to attack this problem in the HW. If you would like the normal distribution table so you can draw the pictures (my preferred way of learning) then I suggest you bookmark this site:

http://www.statsoft.com/textbook/sttable.html

Confidence Interval Estimation

2. Compute a 95% confidence interval for the population mean, based on the sample 1.5, 1.54, 1.55, 1.51, 0.09, 0.08, 1.55, 0.07, 0.99, 0.98, 1.12, 1.13, 1.00, 1.56, and 1.53. Change the last number from 1.53 to 50 and recalculate the confidence interval. Using the results, describe the effect of an outlier or extreme value on the confidence interval.

Hypothesis Testing

The management of the Ceebler Fairy Corporation is considering relocating the corporate office to a new location outside HisWood Forest. Management is concerned that the commute times of the employees to the new office might be too long. The company decides to survey a sample of employees at other companies in the same office forest to see how long these employees are commuting to the office. A sample of 23 employees indicated that the employees are commuting X (bar) = 33 minutes and s = 1 minute, 45 seconds.

Using the 0.01 level of significance, is there evidence that the population mean is above 32 minutes?

What is your answer in (a) if X (bar) = 37 minutes and s = 27 minutes?

Look at your answers for a and b above and discuss what you can learn from the results about the effect of a large standard deviation.

4. Peter’s Updated IT Help company is concerned that the mean wait time of their phone customers for a customer service agent is not greater than 15 minutes. It can be assumed that the population variance is 9 minutes 6 seconds based on past experience. A sample of 563 customers is selected and the sample mean is 16 minutes 30 seconds. Using a level of significance of .10, is there evidence that the population mean wait time is greater than 15 minutes? Fully explain your answer.