Statistics Homework Assignment

This needs to be completed in Excel with details as to how the problem was solved.

 

Thanks in advance

Fall 2013

Problem Set #2
Probability

1. Suppose that the mean of the annual return for common stocks from 2000 to 2012 was 8.5%,

and the standard deviation of the annual return was 25.2%. Suppose also that during the same

12-year time span, the mean of the annual return for long-term government bonds was 1.6%, and

the standard deviation was 7.0%. The distributions of annual returns for both common stocks

and long-term government bonds are bell-shaped and approximately symmetric in this

scenario. Assume that these distributions are distributed as normal random variables with the

means and standard deviations given previously.

a. Find the probability that the return for common stocks will be greater than 2%.

b. Find the probability that the return for common stocks will be greater than 11%.

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 150, 154,

155, 151, 152, 151, 155, 152, 156, and 153. Change the last number from 153 to 201 and

recalculate the confidence interval. Using the results, describe the effect of an outlier or extreme

value on the confidence interval.

Hypothesis Testing

3. The management of XYZ Corporation is considering relocating the corporate office to a new

location outside the Capital Beltway. 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

park to see how long these employees are commuting to the office. A sample of 20 employees

indicated that the employees are commuting X (bar) = 39 minutes and s = 5 minutes.

a. Using the 0.05 level of significance, is there evidence that the population mean is

above 35 minutes?

b. What is your answer in (a) if X (bar) = 42 minutes and s = 20 minutes?

c. 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.

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

4. BestSaladInTown is concerned that the mean wait time of customers for a table is not greater

than 7 minutes. It can be assumed that the population standard deviation is 2.6 minutes based on

past experience. A sample of 340 customers is selected and the sample mean is 7.4 minutes.

Using a level of significance of .01, is there evidence that the population mean wait time is

greater than 7 minutes? Fully explain your answer.