ANOVA for real estate data.

See attached data file.

One Sample Hypothesis Testing Paper - Real Estate

Describe the results of a hypothesis test of one population mean or population proportion.

Team B Bank wants to open a branch in one of the townships based on best price per square footage. They want a test run to see where their best option is.

The Null is all the homes are the same
The alt is one township is better

Ho: T1=T2=T3=T4=T5
H1: Not Ho

Lets use a=.05

Real Estate Date

Describing the results of a hypothesis test of one population mean or population proportion.

Includes the development of the one research question from which we will formulate a research hypothesis.
Team B Bank wants to open a branch in one of the townships... Based on best price per square footage. They want a test run to see where their best option is.

The Null is all the homes are the same
The alt is one township is better

Ho: T1=T2=T3=T4=T5
H1: Not Ho

Lets use a=.05

Hypothesis

In a recent assignment Team B, of one of the classes at the University of Phoenix, began a study of a provided data set related to real estate. Team B will study different variables related to property prices of the homes in the different townships and the correlation to the price per square foot. Team B desires to open the Team B Bank (TBB) one of the townships. The team is presently hypothesizing the price per square footage of the different townships: Township 1, Township 2, Township 3, Township 4, and Township 5 (T1, T2, T3, T4, and T5). Price and square footage are the variables currently under study but other variables included in the data set include: number of bedrooms, number of bathrooms, attached garage, distance from center of town, and presence of a pool. It is possible some of these variables may be used in later studies related to the establishment of TBB. The most influential variables for the current study are square footage and price.
Team B formulated two hypotheses. The null hypothesis is townships 1 through township 5 are all equal in price per square foot. The alternate hypothesis is one township has better pricing per square foot than another township and is not equal to another township relating to price per square foot. Numerically the hypothesis would be reflected as the following: Ho: T1=T2=T3=T4=T5 and H1: Not Ho. Team B decided to run hypothesis tests to determine the most opportune location to open TBB.
Formulate
Starting with the raw data from the web link data sets, team B chose the real-estate data set. With the team B hypothesis in mind the data was adjusted into price, size, and townships. Opening a bank is big business and proper location is important to success, the base data collected is as follows in appendix A. Using the base data the B team can formulate a price per square foot, which is a leading indicator for individuals who are in the market. Appendix B represents the data of price per square foot in relation to each township. The stated null hypothesis is Ho; if the null is selected from the data then we can place our new bank in any townships because the townships are equal. The alternative hypothesis will indicate the townships are not equal, and introduce information to help formulate the direction tree as to which township has the best market for our bank.
 
Appendix A
Price Size Township
125.9 2400 1
139.9 2100 1
147.4 1700 1
176 2200 1
189.4 2200 1
192.6 2200 1
198.3 2100 1
199 2500 1
216.8 2200 1
220.9 2300 1
221.1 2300 1
224 1900 1
224.8 2200 1
232.2 1900 1
245.4 2100 1

Price Size Township
154.3 2000 2
166.2 2000 2
173.6 2100 2
188.3 2100 2
192.2 2400 2
192.9 1900 2
207.5 2100 2
209.7 2200 2
209.7 2200 2
213.6 2200 2
216 2300 2
244.6 2300 2
247.7 2400 2
251.4 1900 2
253.2 2300 2
271.8 2100 2
273.2 2200 2
281.3 2100 2
294 2100 2
307.8 2400 2

Price Size Township
155.4 2400 3
166.5 1600 3
172.4 2200 3
172.7 2200 3
175 2500 3
176.3 2000 3
190.9 2200 3
194.4 2300 3
199.8 2100 3
206 2100 3
217.8 2500 3
221.5 2300 3
233 2200 3
234 1700 3
236.4 2200 3
242.1 2300 3
246 2300 3
246.1 2100 3
254.3 2500 3
263.2 2300 3
289.8 2000 3
292.4 2100 3
294.5 2700 3
312.1 2400 3
327.2 2500 3

Price Size Township
125 1900 4
164.1 2300 4
171.6 2000 4
173.6 2100 4
175.6 2300 4
179 2400 4
179 2400 4
182.4 2100 4
182.7 2000 4
186.7 2500 4
187 1900 4
188.1 1900 4
188.3 2100 4
198.9 2200 4
205.1 2000 4
207.5 2300 4
209 1700 4
209.3 1900 4
227.1 2900 4
240 2600 4
243.7 2700 4
252.3 2600 4
257.2 2100 4
266.6 2400 4
269.9 2200 4
270.8 2500 4
294.3 2400 4
310.8 2900 4
345.3 2600 4

Price Size Township
173.1 2200 5
177.1 1900 5
180.4 2000 5
188.3 2300 5
188.3 2300 5
207.1 2000 5
209.3 2100 5
222.1 2100 5
227.1 2900 5
228.4 2300 5
236.8 2600 5
263.1 2300 5
269.2 2200 5
293.7 2400 5
312.1 2600 5
326.3 2100 5

Performing the hypothesis test
1. Hypothesis
Average price per SqFt in each township
T1= $92.22
T2= $105.12
T3= $103.30
T4= $95.60
T5= $102.38
Mean price per sqft for all townships: $99.79
H0: T1=T2=T3=T4=T5
H1 : ≠ H0
α = .05
2. Since using a two-tailed test, split the risk as shown below:
α/2 = α/.05 = .025
in each tail. Z .05 = ±1.645
Team B will reject H0 if z < +1.645 or if z > -1.645
3. z =
z =
4. Since the test falls outside of the left and right tail, Team B will reject the null hypothesis of H0: T1=T2=T3=T4=T5. In this decision Team B will also conclude that H1: ≠ H0 when at a .05 level of significance.