MAT 315 Statistics

I will not accept the bottling problem for this assignment.

The firm for which you are working is growing. They have announced that they will open facilities in ten states. Those currently working for the firm will have opportunities to re-locate at some of these new facilities. The company is providing information on its policy for cost of living adjustments which are based on the median value of homes.

The company expects to open new locations in the following ten states.

Michigan $119,200

North Dakota $130,500

South Dakota $131,600

Wisconsin $167,200

Maine $173,900

Montana $183,600

Minnesota $185,800

Vermont $215,700

New Hampshire $239,100

Alaska $241,400

The firm has approached you about moving to either Maine or New Hampshire. You will be doing the same job, so there is no increase in salary. They explain that your moving expenses will be paid, but that since your job description will remain the same, you will still receive a salary of $60,000 per year.

When you asked about the cost of living adjustment, your boss explains that the company rule is that if home prices are within the 95% confidence interval of the mean of median home prices for the nation, there will be no cost of living adjustment. The cost of living adjustment is 6%, so in the event that you move to a location where median home prices are outside the confidence interval you will get a 6% adjustment making your new salary $63,600.

You currently live in Idaho and with no family ties, you are interested in making the move. You own your home in Idaho which is fact is valued at the state median of $160,000, a price that is approximately 3 times your income.

Given that you must choose between not moving, or moving to either Maine or New Hampshire, you will have to make some calculations on your own. Of primary concern to you is will you be able to afford a home in the new place comparable to your current home. If you use the financing rule that you can afford a home that is 3 times your income in which location, if any, would you be able to purchase the median value home should you decide to move?

You have assembled the following data and will perform the following statistical analyses to make your decision. 1. Calculate the mean, median, mode, variance, and standard deviation for both the sample and the population. 2. For the population mean construct the 95% confidence interval.

3. Formulate and test a hypothesis that the sample of the ten states has the same mean as the population.

4. Determine if either state location you have been offered, Maine or New Hampshire would result in your receiving a cost of living adjustment.

5. Determine if you would be able to afford the median value home in either location?

Prepare and explain your calculations. Use the evidence to write a paper explaining your decision: don’t move, move to Maine, move to New Hampshire.

Your assignment must follow these formatting requirements:

1. It must be types, double spaces and use Times New Roman font 12

2. It must have one-inch margins on all sides.

3. You are not required to cite references for formulas, definitions, etc.

4. It must have a title page and running header.

Median Property Value by State: Homes 2010-2012 US Census Report Home Value Price In Current Dollars 2010-2012

Alabama $123,400

Alaska $241,400

Arizona $158,100

Arkansas $106,900

California $358,800

Colorado $235,800

Connecticut $278,600

Delaware $235,900

District of Columbia $436,000

Florida $154,900

Georgia $149,300

Hawaii $503,100

Idaho $160,000

Illinois $179,900

Indiana $122,600

Iowa $124,300

Kansas $128,500

Kentucky $120,800

Louisiana $138,800

Maine $173,900

Maryland $289,300

Massachusetts $328,300

Michigan $119,200

Minnesota $185,800

Mississippi $100,000

Missouri $137,100

Montana $183,600

Nebraska $127,800

Nevada $161,300

New Hampshire $239,100

New Jersey $325,800

New Mexico $159,300

New York $286,700

North Carolina $152,800

North Dakota $130,500

Ohio $130,600

Oklahoma $112,900

Oregon $233,900

Pennsylvania $164,700

Rhode Island $245,300

South Carolina $136,300

South Dakota $131,600

Tennessee $138,400

Texas $128,400

Utah $209,000

Vermont $215,700

Virginia $243,100

Washington $256,500

West Virginia $98,300

Wisconsin $167,200

Wyoming $183,200 

Rubric Criteria:

 1. Calculate the mean, median, and standard deviation for both the population and sample median home prices. Weight: 20%

2. Construct a 95% Confidence Interval for the population mean of median home prices. Weight: 25%

3. Conduct a hypothesis test to determine if the sample and population means are the same. Clearly state the logic of your test, the calculations, and the conclusion of your test. Weight: 30% 

4a. Are either or both the median home prices for homes in Maine and New Hampshire within the 95% confidence interval of the population mean? Clearly show and state your conclusion. And

4b. If you conclude that median home prices in one or both Maine and New Hampshire are outside the confidence interval will you be able to buy a median home price if your new salary makes a $199,000 home within your budget? Weight: 15% 

5. Writing / Support for ideas Weight: 5% 

6. Writing / Grammar and mechanics Weight: 5%