Regional vs. National Housing Price Comparison

Regional vs. National Housing Price Comparison Report 2 Introduction Purpose: The purpose of this report is to determine if housing prices and housing square footage in the East South Central region are significantly different from those of the national market. I took a random sample of 100 houses within the region for this report and we are going to use this data to identify if the housing prices in East South Central are higher than the national market as well as if the square footage of homes in the East South Central area are different than the national market. Sample: The random sample of 100 homes from the East South Central region includes the States of Alabama, Kentucky, Tennessee, and Mississippi; the county they are in; the houses listing price; the cost per square foot for the home; and the square footage of the home. Questions and type of test: Let u=mean housing prices in East South Central H0: u=288407 H1: u>288407 a. The population parameter is the mean housing price of the 100 randomly selected homes in the East South Central Region. b. The hypothesis we would like to find is: Is the mean house price in East south Central equal to or higher than the national average. c. We will use a t-test which is a type of inferential statistic used to determine if there is a significant difference between the means of two groups. Regional vs. National Housing Price Comparison Report 3 Let u=mean square footage in East South Central region H0: u=1944 H1: u NOT=1944 a. The population parameter is the mean square footage of the 100 randomly selected homes in the East South Central Region. b. The hypothesis we would like to find is: Is the mean square footage of homes in East South Central equal or different than the national average. c. We will use a t-test which is a type of inferential statistic used to determine if there is a significant difference between the means of two groups, here being the chosen region and the national average. 1-Tail Test Hypothesis: Let u=mean housing prices in East South Central H0: u=288407 H1: u>288407 Significance level=.05 Data analysis: We fail to reject the null hypothesis because the p value is greater than the level of significance. In other words, the mean housing prices in the East South Central are not greater than or equal to the National average, the prices in this area are much lower than the national average. Regional vs. National Housing Price Comparison Report The sample data from the East South Central region has a mean of $234,450 and median of $233,100; most of the houses in this region selected for analysis are very close in price. The standard deviation of 90,900 shows there is not much spread in the data and the shape is symmetric. The normal t-test assumptions have been met: sample size of at least 15 and there are no large outliers or strong skewness. This data is was randomly sampled from the population of the East South Central region and the data variables follow a normal distribution. The central limit theorem states that if you have a population with mean (u) and standard deviation and take 4 Regional vs. National Housing Price Comparison Report 5 sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed; this is true in this case. Hypothesis Test Calculations: Interpretation: The p value (.999999) is much higher than the significance level of .05. We fail to reject the null hypothesis because the p value is greater than the level of significance. The mean housing prices in the East South Central region are not equal to or greater than the national average; they are much lower than the national average. 2-Tail Test Hypotheses: Significance level: .05 U= Mean square footage in East South Central Region H0: u=1944 H1: u NOT=1944 Data Analysis: Regional vs. National Housing Price Comparison Report 6 The sample data from the East South Central region has a mean square footage of 2040 and median of 1999; most of the houses in this region selected for analysis are very close in square footage. The standard deviation of 369.438 shows there is not much spread in the data and the shape is symmetric. The normal t-test assumptions have been met: sample size of at least 15 and there are no large outliers or strong skewness. This data is was randomly sampled from the population of the East South Central region and the data variables follow a normal distribution. The central limit theorem states that if you have a population with mean (u) and standard deviation and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed; this is true in this case. Regional vs. National Housing Price Comparison Report 7 Hypothesis Test Calculations: Interpretation: The p value (.0108) is much less than the significance level of .05. We reject the null hypothesis because the p value is less than the level of significance. The mean square footage of the houses in this region are not equal to the national average, they are significantly higher. Comparison of the Test Results: In order to find the confidence interval I identified the margin of error (confidence.t(.05, standard dev sq footage, sample size) in excel. The margin of error was 73.305, this number is then used to calculate the lower and upper bounds by subtracting and adding to the mean square footage of the region. I am 95% sure that the mean square footage for the East South Central region is between 1967 and 2017. Final Conclusions For the East South Central region, my findings are that the houses are larger and the prices are lower than the national average. Regional vs. National Housing Price Comparison Report 8 I was not very surprised by the findings because I live in the south and I know from research and reading that the housing prices in the south are an incredible amount lower than those in regions such as California, New York and metropolitan cities such as Boston and Chicago.