Report Regional vs National Housing Price Comparison

Regional vs. National Housing Price Comparison Report Introduction Purpose: The purpose of this study is to support the assertions that housing costs in the New England region are higher than the national average and that these homes' square footage is different from that of the average American home. Sample: The sample for this report will be drawn from 100 residences in the New England area using Excel's RAND function on all 1000 of them before selecting 100. Questions and type of test: We will use both 1 and 2 Tailed T tests for this report. We may apply this hypothesis testing technique to both tests (both right-tailed and two-tailed), as our sample size exceeds 30 variables. 1-Tail Test Hypothesis: Does the New England region have greater housing costs than the nation as a whole? $384,430 is the average price of a home in the New England region. The average for the country as a whole is $288,407. Because it is significant that housing costs in the New England region are higher than the national average, I reject the null hypothesis. Data analysis: I determine the average home price to be $384,430 using the random sample calculations in Excel based on 100 randomly selected house prices. The difference between this and the $288,407 national average is $96,000. Data Table Summary Statistics: Is the mean listing price in this region higher than the national average? National Average = $288,407 HO: µ= 288,407 Ha: µ > 288,407 X-Bar $384,430 S 153696.1992 N 100 T 6.247586368 P-Value 5.25846E-09 The summary statistics show that this data is skewed to the right, indicating high-value outliers for this test. The P-value is the significance of 0.5 (95%) in New England, and I reject the null hypothesis. Over $288,407 is the average listing price. Hypothesis Test Calculations: Given that the sample size is sufficient to support it and that we initially lacked knowledge of the population for the standard deviation, this hypothesis test can be conducted. The sample size needed to be between 15 and 30, and we are sampling 100 out of roughly 1000 houses. Interpretation: T.critt 1.98421695 Margin of Error 30496.6604 CI Lower Bound $353,933 CI Upper Bound $414,927 I am 95% confident that the typical price of a home will be in the range of $353,933 and $414,927. This satisfies that condition because the median home price is $384,430. This test is accurate because the mean can be found within the confidence interval. We can't prove that the price of New England Homes is higher than the average home price nationwide because the PValue is so low. 2-Tail Test Hypotheses: In comparison to the national average, square footage differs. The average size of a square foot in the country is 1944SQFT. The typical New England home has 1862 square feet. Due to New England's square footage being significantly less than the rest of the country, we can accept the null hypothesis. Data Analysis: I came to the conclusion that we support the hypothesis that square footage in New England deviates from the national average using the same randomly selected residences. There is an 82SQFT difference between the two. Although statistically close, the data figure demonstrates how significant the discrepancies are to support that theory. Data Table Summary Statistics: Is there a discernible difference between the mean square footage and the national average? 44 is the national average. HO: µ = 1944 Ha: µ =/= 1944 X-Bar 1862.257143 S 259.3436948 N 100 T -3.15191226 P-Value 0.002146548 According to the summary statistics, this distribution is reasonably symmetrical and has tails on both ends that show and accommodate the outliers. We fail to reject the hypothesis since we can observe that the majority of households fall between the national average and the regional average. Hypothesis Test Calculations: Given the sample size in this case, the 2 Tailed test is appropriate. a limit in the center. According to the theorem, this test must have a sample size of at least 30, and our findings must take into account the outliers. Interpretation: T.crit Margin of error 1.984216952 51.45941555 CI Lower Bound 1810.80 CL Upper Bound 1913.72 I have a 95% confidence level that the average New England home is between 1810 and 1913 square feet in size. We must fail to reject the null hypothesis because the null hypothesis is 1944 SQ FT is outside of the data limitations. Based on the sample size, the P-Value is low, and New England Homes are smaller than average. Within the parameters of our testing, there is a discrepancy between the size of the homes and the national average. Comparison of the Test Results: The red dot represents the average national price of $288,407 and average square footage of 1944 SQ FT. The results of the hypothesis testing show that, according to our sample, most residences in New England are both smaller and more expensive than those nationwide. The diversity of homes' sizes and prices widens until the national average is reached (see scatter plot above). Final Conclusions I anticipated seeing a considerably wider range of results with the outliers taking center stage while taking into account only 10% of the sample size of the data. The few who argued in favor of the proposition that overall size affects housing prices were taken into account by the confidence interval testing. But compared to other parts of the country, the New England region is much more densely inhabited, and as a result, houses are typically smaller and closer together.