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 relocate 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?