**All of your work should be contained in ONE Excel spreadsheet (though you are welcome to use a separate tab for each question).** Put all of your details in the Excel file. You should be using the formulas in Excel, too. It’s extremely important for you to learn to use the many features of Excel.

**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 .6%, and the standard deviation was 2.1%. The distribution 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.

*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. If you would like the normal distribution table so you can draw the pictures, then you may want to bookmark this site: http://www.statsoft.com/textbook/sttable.html. (You may need to copy and paste the URL into a new browser session.)

** **

**Confidence Interval Estimation**

**2.** Compute a 95% confidence interval for the population mean, based on the following sample: **1.5, 1.54, 1.55, 1.51, 0.09, 0.08, 1.60, 0.17, 0.99, 0.98, 1.12, 1.13, 1.00, 1.56, and 1.53**. Change the last number from 1.53 to 50.00 and recalculate the confidence interval. You should report the upper and lower limits for __both__ __sets__ of numbers. Using the results, *describe the effect of an outlier or extreme value on the confidence interval (when comparing the confidence intervals for the first and second set of numbers)*.

__Hint__**: A confidence interval and a confidence level are NOT the same thing. (Again, a confidence interval should have lower and upper limits, and I want you provide the upper and lower limits for both sets of numbers.)**

** **

**Hypothesis Testing**

**3. ** 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 decided 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.

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

*b. What is your answer in Part A if instead X (bar) = 37 minutes and s = 27 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.*

* *

__Reminder__**: Please use the six steps for hypothesis testing as outlined in your Lind textbook. Yes, that means I want you to label and discuss each step (Step 1, Step 2, etc.).**

**4. **Peter’s new 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 and 6 seconds based on past experience. A sample of 563 customers is selected and the sample mean is 16 minutes and 30 seconds. *Using a level of significance of .05, is there evidence that the population mean wait time is greater than 15 minutes? *Fully explain your answer.

__Reminder__**: Please use the six steps for hypothesis testing as outlined in your Lind textbook. Yes, that means I want you to label and discuss each step (Step 1, Step 2, etc.).**

Subject | Mathematics |

Due By (Pacific Time) | 09/01/2015 05:00 pm |

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