Advanced Hypothesis Testing

Advanced Hypothesis Testing

This report is a continuation from the previous week statistical report and entails more detailed information concerning the mean costs of the average rent price for office spaces in and around the Sacramento area. A business plan is being designed to include financial coverage and location.

This reportÐŽ¦s primary focus is to base the cost of office space strictly upon price, to ascertain the startup and ongoing costs of the short-term business plan. However, certainly we will consider other issues with the overall plan once the median is found. Other issues to be considered aside from costs are location, convenience, fixtures, insurance prices, and customer accommodations. Surrounding areas of Sacramento will allow access to more build sites, but the downside is possible poor location for city dwellers.

Last week in AdamÐŽ¦s quest of moving his home based business into an office setting, he compared the mean price from the local on-line real estate listings to the price information from his sample of 20 office rooms. Through a t-test statistical analysis, Adam could not conclude that the mean price for the office space in Sacramento is more than $680. However, before Adam makes the final decision, he decides to do a little more investigation based upon a sampling of 20 prices of offices in outlying areas of Sacramento.

This week Adam will formulate a hypothesis statement and perform the five-step hypothesis test on the data he collected. After completing his analysis of the 22 prices from outlying areas, and 20 office prices of Sacramento, he will be able to find out if the office prices in surrounding area of Sacramento area is cheaper then the prices of Sacramento.

Prices from Sacramento

600 760 890 580 950 440 876 998 555 765

985 725 490 875 495 560 580 775 890 755

Prices from surrounding area of Sacramento

960 650 690 580 850 540 775 898 500 465 450

785 780 490 775 495 660 580 775 890 900 560

Step 1: State the null hypothesis and the alternate hypothesis.

- Null hypothesis: The mean price for office space in surrounding area of Sacramento is greater than or equal to the mean price of Sacramento.

- Alternate hypothesis: The mean price for office prices in surrounding area of Sacramento is smaller then the mean price of Sacramento.

H0: Ñ"Э1 > Ñ"Э2 Outlying areas = 1

H1: Ñ"Э1 < Ñ"Э2 Sacramento = 2

Step 2: Select the level of significance.

Adam will be using the 0.05 level of significance.

Ñ"С = .05

Step 3: Select the test statistic.

Adam will be using the t-test statistic.

n1 = 22

n2 = 20

t Statistic

df = n1 + n2 ÐŽV 2 = 40

Step 4: Formulate the Decision Rule.

Reject H0 and Accept H1 if tcal is < tcrit (-1.684)

Sp2 = 28854.73

tcal = - 0.823

Step 5: Make a decision and interpret the result.

H0 is not rejected since tcal (-0.823) > tcrit (-1.684). Therefore the mean for office prices in surrounding area of Sacramento is not cheaper then the mean price of Sacramento.

Based upon the information found in the cost analysis, office location prices are quite similar in the inner and outer rim areas. One can assume now with good probability that finding good office space for the real estate brokerage can be based solely upon choice without too much consideration on median cost for space. The cost should not affect the decision