MAT 240 Module 5-3 Assignment

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Hypothesis Testing for Regional Real Estate Company 1 Hypothesis Testing for Regional Real Estate Company Tiana Rodriguez Southern New Hampshire University

Hypothesis Testing for Regional Real Estate Company 2 Introduction The purpose of this analysis is to prove to the head of Regional Real Estate Company that the advertisement by said salesman is worth the average cost per square foot of home sales based on $280. In order to do so I must generate a random sample size of 750 houses using data for the Pacific region and use this data to perform a hypothesis test. I have used the rand function to be able to receive the most random data possible from smallest to largest. Hypothesis Test Setup The population Parameter of interest is the mean (average) price of houses in the Pacific region. The null hypothesis states that the population mean price of houses in the Pacific region is equal to the target value of $280,000. The alternative hypothesis states the population mean price of houses in the Pacific region is not equal to $280,000, this is the two-tailed test. I will perform a two-tailed t-test. Data Analysis Preparations The Sample summary consists of 750 houses from the Pacific Region. The sample mean and Target is $263,000, the median is $202,000 and the standard deviation is $159,000. The standard error is $5.81. The Histogram sample shows a normal distribution with a slightly skewed right tail. The center of the distribution is around $263,000 and the spread is about $159,000. The assumptions are

Hypothesis Testing for Regional Real Estate Company 3 based on the random selections, thus making it normally distributed, with the assumption of the population standard deviation unknown. We will use the significance level of 0.05. To calculate the p-value we use this equation (mean-target)/(standard error), while using the t-distribution and degree of freedom(749), we calculate the p-value. Calculations Excel Function Type of Test =T.DIST.RT([test statistic], [degree of freedom]) Right-tailed =T.DIST([test statistic], [degree of freedom], 1) Left-tailed =T.DIST.2T([test statistic], [degree of freedom]) Two-tailed [ Note: The degree of freedom is calculated by subtracting 1 from your sample size.]

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Hypothesis Testing for Regional Real Estate Company 4 On the Normal curve graph. The test statistic would be located where it corresponds to the t- statics and the p-value represents the area under the curve.

Hypothesis Testing for Regional Real Estate Company 5 Test Decision If the p-value is less than or equal to the significance level (a=0.05), we reject the null hypothesis, in which we failed to reject the null hypothesis. Based on the analysis, comparing both p-value and significance level, if the p-value is greater than <0.05 we reject the null hypothesis, concluding that there is indeed a difference between the average price of houses with the target value of $280,00. In our instance the p value is not greater than >0.05 which we fail to reject the null hypothesis, that indicates that there is not enough evidence to conclude a significance between the average and the target value. Conclusion

Hypothesis Testing for Regional Real Estate Company 6 We discovered that the test's p-value did not reach statistical significance after running a two- tailed t-test on a randomly selected sample of 750 houses in the Pacific region at a significance level of 0.05. In particular, the p-value exceeded 0.05. We are unable to reject the null hypothesis as a result. This implies that there is insufficient data to draw the conclusion that the typical cost of houses in the Pacific area deviates considerably from the desired amount of $280,000. The sample mean does not meet the target value of $263,000, but at the chosen significance level, there was no statistically significant difference. It might take more information and analysis to reach a firmer conclusion, pertaining to Pacific region housing costs.

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