Housing prices case study

I’m studying for my Statistics class and don’t understand how to answer this. Can you help me study?

• Download the .pdf and .xlsx files from Blackboard, along with this .docx.

• Analyze the dataset, identify key questions and write a report based on your findings.
• Use any (more than one) technique covered so far in class.
  • For e.g. use two sample tests, ANOVA, chi-sq. tests, and multiple regression.

Guidelines for Report

• Type your report in a clear and organized style:
• The score of the written report will be weighted as follows:
• For the statistical analysis, address:

• Section 1, Executive Overview (0.5-1 page):Summarize the key findings based on your study and discuss any possible future study or data collection that might be necessary.
• Section 2, Statistical Analysis (3-5 pages):Very carefully describe the steps you took to analyze the data and describe what, how and why decisions were made along the way.Support your analysis with relevant plots, relevant statistics, and relevant hypothesis tests.Include these in your report. DO NOT include irrelevant calculations or analyses.All relevant computer outputs can be relegated to the appendices with clear cross-referencing in the paper.(Housing prices case study)
• Section 3, Summary and Conclusion (0.5-1 page): Summarize how the results of your analysis may be used in managerial decision-making.Also discuss what you have learned in the course of completing the project and how these experiences can be applied in future undertakings of statistical analysis.

Section 1: 20%

Section 2: 50%

Section 3: 20%

Writing: 10%

• Identify multiple question from your data.
• State the hypothesis for each question.
• Run the appropriate statistical procedure for each question.
• Report the results, and summarize the findings for each question.
• Interpret the results in the context of your question.

You should assume that you are writing the report to a manager that knows very little about statistics. Your writing should present the statistical findings in a way that even a layperson can understand.

Solution

Report: Regional vs. National Housing Price Comparison

Introduction

The aim of this assignment is to apply statistical approaches to address research issues and conduct hypothesis testing to address an authentic problem. During the assignment, I will be playing the role of a data analysist hired to determine if my region’s housing prices and housing square footage are significantly different from those of the national market. The following questions will be addressed in the report:(Housing prices case study)

1. Are the housing prices in my regional market higher than the national market?

Hypothesis: South Atlantic region housing prices is greater than the national averages

H1: μ > $288,407

1. Is the square footage for homes in my region different than the average square footage for homes in the national market?

Hypothesis: South Atlantic region square footage is not equal to the national averages.(Housing prices case study)

H2: μ ≠ 1,944

1. For my region, what is the range of values for the 95% confidence interval of square footage for homes in my market?

Random sample was extracted from the South Atlantic Region. To obtain the random sample, I used the RAND () function in excel. The main variables of interest considered were house listing price, cost per square, and square footage. To answer the questions listed above, hypothesis testing will be used. A 95% confidence level will be used while testing the designed hypotheses.(Housing prices case study)

1-Tail Test

The first question focuses on determining if the housing prices in my regional market are higher than the national market average. The hypothesis that will be tested for this question are:(Housing prices case study)

Null hypothesis (Ho): μ = $288,407

Alternative hypothesis (Ha): μ > $288,407

This will be a right-tailed test with a 0.05 significance level – the likelihood of rejecting the null hypothesis when it is true.

House listing prices for South Atlantic region is concentrated between $173K and 263K. The mean, standard deviation, and median house listing prices for the national market are higher than those of my regional market (South Atlantic). The histogram is skewed to the right. The right tail is longer than the left tail. This indicates that the mean is higher than the median.(Housing prices case study)

Hypothesis Test Calculations

The standard error is obtained as follows: (standard deviation/sqrt (sample size)

= 119617/sqrt100

= 11961.70

The value of the test statistic is obtained as:

T = (272786- 288407/11961.7)

= -1.31

Using the T.DIST.RT function, the p value is obtained as 0.90269734.

Interpretation:

The p value obtained is higher than the significance level 0.05. Therefore, the null hypothesis is not rejected. This means that the house listing prices in South Atlantic is not higher than the national market average.(Housing prices case study)

2-Tail Test

The aim of the 2-tailed test is to establish if the square footage of homes in South Atlantic are different than the national averages. To do this, the following null and alternative hypotheses will be tested:(Housing prices case study)

Ho: μ = 1944

Ha: μ > 1944

A 0.05 significance level will be used. The same sample used for the 1-tail test will be used for this test.

The data is concentrated between 1,768 and 2,038. The right tail of the histogram is taller than the left tail. This implies that the data is skewed to the right – the mean is higher than the median. The mean square footage for South Atlantic (2005 feet) is higher than that of the national market (1,944 feet). The median square footage for South Atlantic (1,961) is also larger than that of the national market (1,901 feet). (Housing prices case study)

Hypothesis Test Calculations

The standard error is obtained as follows: (standard deviation/sqrt (sample size)

= 362.14/sqrt100

= 36.21

The value of the test statistic is obtained as:

T = (2005-1944/36.21)

= 1.69

Using the T.DIST.2T function, the p value is obtained as 0.09488065.

The obtained p value is 0.095. This value is greater than the alpha value used (0.05). Therefore, the null hypothesis is not rejected. There is no sufficient evidence that square footage of houses in South Atlantic are significantly different than the national square footage.(Housing prices case study)

Comparison of the Test Results

Additionally, the company wanted to know the range of values for the 95 percent confidence interval of square footage for residences in the South Atlantic region. I did this by multiplying the 95 percent confidence interval, which was 1.96, by the standard error. Thus, I multiplied 36.21 by 1.96 to obtain 70.98. This enabled me to compute the confidence interval’s lower and upper bounds, which I accomplished by subtracting 70.98 from 2,005 (sample mean) and then adding 70.98 to 2,005. I obtained a lower limit of 1,934 and an upper limit of 2,076 using the 95 percent confidence interval.(Housing prices case study)

Final Conclusions

After conducting the required test, I feel the company has obtained the answers it required. The company initially sought to determine whether South Atlantic house prices were higher than national market averages. That was not the case. The South Atlantic average was slightly lower than the national average. Additionally, the company sought to discover whether the square footage of homes in the South Atlantic differed significantly from national averages. South Atlantic averages were slightly higher than national averages, with the lower limit being within the national average’s. the third question was about the computing the 95% confidence interval.  I obtained a lower limit of 1,934 and an upper limit of 2,076 using the 95 percent confidence interval.(Housing prices case study)

Reference

https://www.ncbi.nlm.nih.gov/