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Hypothesis Testing Paper (A one sample test)
Learning Team A
Brian Cardinal, Phillip R. Gideon, and Venus Wilson
University of Phoenix
RES/343 Research and Evaluation
Professor Gerald Rintala
July 13, 2009
Rodger's Realty is looking to purchase property in Kansas City, Missouri, USA. The mean home value for the entire United States is $210.00k. Lisa, the senior investment strategist, will only recommend purchasing investment properties in towns where the mean home value is higher than the national average. In her search for new investment properties, Lisa decided to look at housing data for Kansas City, Missouri. She believes that the average home price of 221.10k in Kansas City, Missouri, 11.10k higher than the national average of 210.00k, is not due to chance. Before testing her hypothesis, she set her level of significance at .05 which results in a critical value of 1.65.
The null hypothesis for Lisas research is that the home values in Kansas City, Missouri are less than or equal to the national average. The alternate hypothesis for her experiment is that the home prices in Kansas City, Missouri are higher than the national average. Ho: < 210.00 versus H1: > 210.00. To test her null hypothesis, Lisa drew a random sample of 105 home prices from the population of Kansas City, Missouri to compare against the national average home value of 210k. For her sample of 105 home prices, Lisa used the Z-statistic for a right-tailed hypothesis test because her sample size is greater than 30 and only the sample standard deviation is known.
Before calculating the Z-statistic for her sample, Lisa needed to find the standard deviation of her sample which is 47.11. With her sample data together, Lisa established a decision rule before testing her hypothesis. She concluded the following: Ho is rejected if Z > 1.65. Next she inputted the data from her sample into the formula for a one-tailed Z-test:
Z = 221.1 210.00 = 11.1__ = 2.42
47.11/"105 4.596
To get a better idea of the strength of her evidence, Lisa decided to find the P-value for her computed Z-score of 2.42 which came out to P = .0078. With her computed Z of 2.42 being greater than the critical Z of 1.65, she can reject the null hypothesis. Additionally, with a P-value of .0078 being less than her .05 level of significance, the chance of her falsely rejecting the null hypothesis is only 78 in 10,000 a very convincing number.
Although Lisa was happy with her findings, she decided that she wanted to dig down even deeper and draw a random sample of 15 from her original sample of 105 to use for T-test analysis. In this mini-sample, Lisa found a mean home value of 239.06k with a standard deviation of 47.09k. She then inputted this new data into the formula for a one sample, right-tailed T-test as follows:
T = 239.06 210.00____ T = 29.06 T = 2.39
47.09 12.168
"15
The critical T for = .05 and V = 14 is 1.761.
The P-value for = .05 at 14DF is .0315
Her hypotheses for this one sample T-test are:
Ho: < 210.00 versus H1: > 210.00
The results from Lisa s one sample T-test indicate that she can reject the null because:
T = 2.39 > critical T of 1.76 and P = .0315 < = .05 which is also very convincing.
This study can be exploited in different categories. To understand the preference of Lisas strategy, it would be suited to provide choices that parallel with the demand choice of investment homes on the market for sale. Lisa who would like to initiate purchasing investment properties is seeking certain specifications to which the mean indicates the average home asking price is $239.06K; Lisa can determine the location provided if the sellers demand is elevated based on community variables and comparisons. Strategic planning, decision making and analytical skills can best assure the hypothesis testing is advantageous.
The benefits of this research are not limited just to the resale investment and housing median markets. Lisa who is currently analyzing investment properties can also expand her horizons by examining newer communities appealing to future leasing or rental consumers and available property lots to build inducing the community patronage of new real estate as well. Investment properties are a positive generating income depending upon imperative criteria stipulating requirements such as public transportation commute mileage to the closest city or town, safe, and up and coming friendly neighborhood atmosphere. Having the ability to add additional amenities and or space generating instant equity to the investment property by preparing calculations by sketching cost factors, financial planning, and future prosperity could be a positive business investment for Lisas firm.
Due to the US economy induced by the financial markets, the profound slump of housing, high unemployment, and the decline of consumer spending. This has caused concern for consumer and home owner in the real estate industry. Even in this downturn, there are people and investment realtors as like Lisa who is looking for homes in this buyers market. Based on the sluggish US economy, there is an abundance of dwellings available for purchase created by high unemployment, mortgage delinquencies and foreclosures.
Due to the excess number of homes on the market, Lisa is able to acquire more amenities, such as additional square footage, a pool, additional bedrooms, bathrooms and basement. Even in this delayed economy, those additional amenities all have an impact on the investment property demand price of an investment property.
Conclusion
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