# Two Sample Hypothesis

**Topics:**Non-parametric statistics, Statistics, Statistical hypothesis testing

**Pages:**5 (1370 words)

**Published:**March 29, 2011

Team B

RES 342

Eric Hogan

University of Phoenix

Nonparametric Hypothesis Testing

Nonparametric testing does not depend on certain data in a particular distribution. Also, nonparametric testing applies techniques that do not assume that the basis of a model is predetermined. In a previous paper we discussed a hypothesis with single and double samples. Now we will conduct the equivalent, nonparametric test of the real estate hypothesis using another five-step process. The testing we will use in this paper will be the Wilcoxon Signed-Rank Test. The Wilcoxon Signed-Rank Test compares a single sample median with a benchmark using only ranks of data instead of the original observations. It is used to compare paired observations. An advantage of the Wilcoxon Signed-Rank Test is the freedom from the normality assumption. Other advantages are robustness to outliers and applicability to ordinal data (David P. Doane, 2007). In the Wilcoxon Signed-Rank Test the population should have a lot of similarity. The data should have some correlation like houses and price for example. Our hypothesis is as stated: If a real estate home has 3 bedrooms or more, then the price is at least 200,000 dollars or more. The possible outcomes for the tests are left-tailed, two-tailed and right-tailed. The intention of this assessment is to increase knowledge of respective research. The Wilcoxon test is a nonparametric test that tested the difference between each set of pairs, and analyzes only the differences between the paired measurements for each subject. The whole point of using the Wilcoxon Signed-Rank test is to control the experimental variability, and therefore increase the power. Factors that don’t have control in the experiment will affect the before and after the measurements equally.

Within the housing sector these days is very important that homes are competitively priced, and along with taking into consideration the venue. The aspect from a customer that may impact the cost of a house, the real estate procedure can increase the cost efficiency. Team B are now initially determines the aim of the study and after the examines the outcomes by performing the five step hypothesis using the Wilcoxon Signed- Rank Test will express the hypothesis, express the selection principle, compute the predicted frequencies, compute the test statistic, and take the final decision based on reject or not rejected. Step One: State the null and alternate hypothesis

Null and Alternate Hypothesis: The median cost of a home with four bedrooms is less than or equal to $200 Ho: n < 200

H1 : n > 200

In hypothesis testing, the significance that use to for rejecting the null hypothesis can be chosen arbitrarily from the commonly used ones like 5% (α=0.05), 1% (α=0.01) and 0.1% (α=0.001). The lower the significance level, the more the data must diverge from the null hypothesis to be significant. Therefore, α= 0.01 level is more conservative than an alpha= 0.05 level. We choose Significance Level, a = 0.05 Step Two: Choosing the test statistic

W+ = 329

W- = 167

Sum of all Ranks,=0.5n(n+1)=0.5 ×31×(31+1)=496

W_++W_-=329+167=496

Expected Value,E(W_stst )=0.5×0.5×n(n+1)=0.5×0.5×31×(31+1)=248 If the Null Hypothesis were true, we would expect W_+ and W_- to have roughly the same value. There are two possible test statistics, W_+=329 and W_-=167 and we have to decide which one to use. Since the alternate hypothesis is η>200, we are interested in W_-, sum of the ranks less than the median value. W_+ is much greater as compared to W_-, thus a greater number of homes with 4 bedrooms have a price greater than $200. W_stat=W_- =167

Sample Size, n =31

Since the sample size, n >30, we can use a normal approximation in this case with μ_W=n(n+1)/4=31(31+1)/4=248

σ_W=√(n(n+1)(2n+1)/24)=√(31(31+1)(2×31+1)/24)

If two or more observations are equal, then the variance must be reduced by...

References: David P. Doane, L. E. (2007). Applied Statistics. New York, NY: McGraw-Hill Irwin.

University of Phoenix. (2007). Applied Statistics in Business and Economics. Retrieved from University of Phoenix, RES342 - Research and Development website.

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