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Feb 20, 2024

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Introduction: Region: Our project is focused on analyzing the housing market in the East North Central region. Purpose: The objective of this analysis is to identify any significant disparities between the housing market in the East North Central region and the national housing market. Sample: We will randomly select 500 house sales (=rand()) from the states of Illinois, Indiana, Michigan, Ohio, and Wisconsin within the East North Central region. Questions and type of test: A. Hypothesis 1: Population Parameter: Average housing prices in the East North Central region. Hypothesis: Are housing prices in the East North Central region lower than the national average? Type of Test: One-tailed. B. Hypothesis 2: Population Parameter: Average square footage in the East North Central region. Hypothesis: Does the square footage of homes in the East North Central region differ from the national average? Type of Test: Two-tailed. Level of confidence: To address the problem at hand, we will employ estimation and confidence intervals. These methods will allow us to calculate the margin of error for our sample mean and construct a 95% confidence interval for our findings. A 95% confidence level will enable us to draw accurate conclusions about the population parameters based on our sample data, minimizing the risk of incorrect interpretations. Furthermore, confidence intervals will provide us with a range of values for our results, enhancing our understanding of the data and its significance. Overall, these techniques will facilitate a comprehensive analysis of the housing market in the East North Central region and its comparison to national averages, ensuring a thorough and reliable study. 1-Tail Test Hypothesis: In this 1-tail test, we hypothesize that the average housing prices in the East North Central region are lower than the national average. Population Parameter: Average housing prices in the East North Central region. Null Hypothesis (Ho): The average housing prices in the East North Central region are not lower than the national average. Alternative Hypothesis (Ha): The average housing prices in the East North Central region are lower than the national average.

Significance Level: α = 0.05 Data Analysis: We conducted a random sample of 500 house sales from the East North Central region and obtained the following information: Histogram of Sample Data: Housing prices in the East North Central region Summary Statistics: Sample Size: 500 Sample Mean: $194,621 Sample Median: $179,950 Sample Standard Deviation: $80,326 Standard Error: $3,592 Quartile 1: $129,975 Quartile 3: $245,743 National Comparison: National Average Listing Price: $288,407 Median: $249,940 Standard Deviation: $172,779 Q1: $182,725 Q3: $334,640 Shape, Center, and Spread: Based on the histogram and summary statistics, the sample data appears to be right-skewed. The center of the data, represented by the median of $179,950, is relatively close to the national median of $249,940. However, the spread of the data, indicated by the standard deviation and quartile values, is smaller compared to the national standard deviation of $172,779. This suggests that housing prices in the East North Central region may be more consistent compared to other regions. Checking Conditions: Normal Condition: The shape of our sample data does not follow a normal distribution. Other Conditions: We considered the central limit theorem and our random sampling method. With a random sample of 500 house sales from the region, we can assume that our sample is representative of the population and meets the necessary conditions for conducting a hypothesis test. Hypothesis Test Calculations: Using the formula (mean – target)/standard error, we calculated the test statistic (t): t = ($194,621 - $288,407) / $3,592

t = -26.11 Using the T.DIST function in Excel with a degree of freedom of 499 (500-1), we calculated the probability (p-value): p = T.DIST(-26.11, 499, True) p = 1.13462E-95 Interpretation: The p-value of 1.13462E-95 is significantly lower than our significance level of α = 0.05. Therefore, we reject the null hypothesis (Ho) and find enough evidence to support our alternative hypothesis (Ha) that the average housing prices in the East North Central region are lower than the national average. This conclusion aligns with our initial hypothesis and demonstrates a significant difference between regional and national housing prices. Relating p-value and Significance Level: The extremely low p-value of 1.13462E-95, compared to our significance level of α = 0.05, indicates that the probability of obtaining a result as extreme or more extreme than our sample data by chance is extremely unlikely. Decision: Based on our interpretation and conclusion, we reject the null hypothesis and accept the alternative hypothesis. Conclusion: Our results provide evidence to support the claim that the average housing prices in the East North Central region are lower than the national average. This difference may be influenced by various factors such as location, market demand, and regional economic conditions. Two-tailed test Hypotheses: For this test, we have the null hypothesis (Ho) stating that the population mean (μ) is $288,407, and the alternative hypothesis (Ha) stating that μ is not equal to $288,407. Significance level: We will maintain a significance level of α = 0.05, which provides a 95% confidence level for our test results. Data analysis: Upon analyzing the sample data, we observe that the distribution is not normal and shows a potential right skewness. Histogram of sample data: The histogram reveals the following details: National Average Square footage: 1,944 Median: 1,899 Standard Deviation: 385 Q1: 1,717 Q3: 2,132 Sample Mean: 2,012 Median: 1,729

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Standard Deviation: 384 Standard Error: 17.16 Q1: 1,566 Q2: 1,971 Summary of sample data: In comparison to the national data, our sample exhibits a slightly higher mean and median, similar Q1 and Q3 values, and a comparable standard deviation. The distribution also appears to be skewed to the right. Assumptions: Based on our sample size of 500 and the central limit theorem, we can assume the distribution is approximately normal. Additionally, the sampling method used is random, indicating a representative sample of the population. Hypothesis test calculations: Test Statistic (t): (mean - target) / standard error = (2,012 - 1,944) / 17.16 = 3.96 Probability (p): By utilizing the TDIST.2T function in Excel, we derive a p-value of 8.48758E-05. Interpretation: The p-value is significantly lower than our significance level of 0.05, suggesting an extremely low probability of obtaining a result as extreme or more extreme than our sample data by chance. Hence, we reject the null hypothesis and accept the alternative hypothesis. Comparison of p-value and significance level: The p-value is much lower than our significance level of 0.05. Decision: Based on our interpretation and conclusion, we reject the null hypothesis and accept the alternative hypothesis. Conclusion: Our results provide sufficient evidence to support the claim that the average square footage for homes in the East North Central region is not equal to the national average of 1,944 square feet. Comparison of test results: To calculate the 95% confidence interval for our sample, we use the formula: Sample mean ± t * (standard error). Our margin of error is 33.71376453, resulting in a confidence interval of approximately (1,978 - 2,046). This implies that we are 95% confident that the true mean of square footage for homes in the East North Central region falls within this range. This range is wider than the national average, which falls within approximately (1,865 - 1,932). Thus, we can infer that there is more variability in square footage for homes in the East North Central region compared to the national average. Final Conclusions of Project Based on our research, we have found that the average listing price in the East North Central region is significantly lower than the national average. This suggests that homes in this region may offer more affordability compared to other parts of the country. Furthermore, the square footage in the East North

Central region does not align with the national average. The confidence interval for this region is also wider, indicating a greater variability in square footage when compared to the national average. These findings do not come as a surprise, considering that the East North Central region includes states such as Michigan and Ohio, which are renowned for their more affordable housing prices. Additionally, it is important to note that national averages can be influenced by higher-priced regions, which can skew the overall perspective.

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