Apply statistical techniques & Perform hypothesis testing

at
Categories
Tags

 

Apply inference methods for means to test your hypotheses about the housing sales market for a region of the United States. You will use appropriate sampling and statistical methods.

Scenario
You have been hired by your regional real estate company to determine if your region’s housing prices and housing square footage are significantly different from those of the national market. The regional sales director has three questions that they want to see addressed in the report:

Are housing prices in your regional market lower than the national market average?
Is the square footage for homes in your region different than the average square footage for homes in the national market?
For your region, what is the range of values for the 95% confidence interval of square footage for homes in your market?
You are given a real estate data set that has houses listed for every county in the United States. In addition, you have been given national statistics and graphs that show the national averages for housing prices and square footage. Your job is to analyze the data, complete the statistical analyses, and provide a report to the regional sales director. You will do so by completing the Project Two Template located in the What to Submit area below.

Directions
Introduction

Region: Start by picking one region from the following list of regions:
West South Central, West North Central, East South Central, East North Central, Mid Atlantic
Purpose: What is the purpose of your analysis?
Sample: Define your sample. Take a random sample of 500 house sales for your region.
Describe what is included in your sample (i.e., states, region, years or months).
Questions and type of test: For your selected sample, define two hypothesis questions (see the Scenario above) and the appropriate type of test for each. Address the following for each hypothesis:
Describe the population parameter for the variable you are analyzing.
Describe your hypothesis in your own words.
Identify the hypothesis test you will use (1-Tail or 2-Tail).
Level of confidence: Discuss how you will use estimation and confidence intervals to help you solve the problem.
1-Tail Test

Hypothesis: Define your hypothesis.
Define the population parameter.
Write null (Ho) and alternative (Ha) hypotheses. Note: For means, define a hypothesis that is less than the population parameter.
Specify your significance level.
Data analysis: Summarize your sample data using appropriate graphical displays and summary statistics and confirm assumptions have not been violated to complete this hypothesis test.
Provide at least one histogram of your sample data.
In a table, provide summary statistics including sample size, mean, median, and standard deviation. Note: For quartiles 1 and 3, use the quartile function in Excel:
=QUARTILE([data range], [quartile number])
Summarize your sample data, describing the center, spread, and shape in comparison to the national information (under Supporting Materials, see the National Summary Statistics and Graphs House Listing Price by Region PDF). Note: For shape, think about the distribution: skewed or symmetric.
Check the conditions.
Determine if the normal condition has been met.
Determine if there are any other conditions that you should check and whether they have been met. Note: Think about the central limit theorem and sampling methods.
Hypothesis test calculations: Complete hypothesis test calculations.
Calculate the hypothesis statistics.

Sample Solution

Project Two Template: Real Estate Market Analysis

Introduction

  • Region: East North Central (ENC)
  • Purpose: The purpose of this analysis is to determine if housing prices and square footage in the East North Central region are significantly different from the national market averages and to provide a range of values for the 95% confidence interval of square footage for homes in this region.
  • Sample: A random sample of 500 house sales from the East North Central region was selected from the provided real estate dataset.
    • The East North Central region includes the states of Wisconsin, Michigan, Illinois, Indiana, and Ohio.
  • Questions and Type of Test:
    • Question 1: Are housing prices in the East North Central regional market lower than the national market average?
      • Population Parameter: Average housing price in the national market.
      • Hypothesis: The average housing price in the East North Central region is lower than the national average.
      • Hypothesis Test: 1-Tail (left-tailed) test.
    • Question 2: Is the square footage for homes in the East North Central region different than the average square footage for homes in the national market? 1
      • Population Parameter: Average square footage of homes in the national market.
      • Hypothesis: The average square footage of homes in the East North Central region is different from the national average.
      • Hypothesis Test: 2-Tail test.

       

      1. www.studocu.com
      www.studocu.com
  • Level of Confidence: A 95% confidence interval will be used to estimate the range of values for square footage in the East North Central region. This interval will provide a range within which we are 95% confident the true population mean falls.

1-Tail Test (Housing Prices)

  • Hypothesis:
    • Population Parameter: National average housing price.
    • Null Hypothesis (Ho): μ_ENC ≥ μ_National (The average housing price in the ENC region is greater than or equal to the national average.)
    • Alternative Hypothesis (Ha): μ_ENC < μ_National (The average housing price in the ENC region is less than the national average.)
    • Significance Level: α = 0.05
  • Data Analysis:
    • Histogram: (Provide a histogram of the sample housing prices from the ENC region)
    • Summary Statistics Table:
      • Sample Size (n): 500
      • Mean (x̄): (Calculate the sample mean)
      • Median: (Calculate the sample median)
      • Standard Deviation (s): (Calculate the sample standard deviation)
      • Quartile 1: (Calculate quartile 1)
      • Quartile 3: (Calculate quartile 3)
    • Summary of Sample Data:
      • Compare the sample mean, median, and standard deviation to the national averages.
      • Describe the shape of the histogram (skewed or symmetric).
    • Check Conditions:
      • Normal Condition: Check if the sample size is large enough (n ≥ 30) for the Central Limit Theorem to apply.
      • Other Conditions: Check for random sampling, and independence of samples.
  • Hypothesis Test Calculations:
    • Calculate the t-statistic: t = (x̄ – μ) / (s / √n)
    • Determine the degrees of freedom: df = n – 1
    • Find the p-value using the t-statistic and degrees of freedom.
    • Compare the p-value to the significance level (α).

2-Tail Test (Square Footage)

  • Hypothesis:
    • Population Parameter: National average square footage.
    • Null Hypothesis (Ho): μ_ENC = μ_National (The average square footage in the ENC region is equal to the national average.)
    • Alternative Hypothesis (Ha): μ_ENC ≠ μ_National (The average square footage in the ENC region is different from the national average.)
    • Significance Level: α = 0.05
  • Data Analysis:
    • Histogram: (Provide a histogram of the sample square footage from the ENC region)
    • Summary Statistics Table:
      • Sample Size (n): 500
      • Mean (x̄): (Calculate the sample mean)
      • Median: (Calculate the sample median)
      • Standard Deviation (s): (Calculate the sample standard deviation)
      • Quartile 1: (Calculate quartile 1)
      • Quartile 3: (Calculate quartile 3)
    • Summary of Sample Data:
      • Compare the sample mean, median, and standard deviation to the national averages.
      • Describe the shape of the histogram (skewed or symmetric).
    • Check Conditions:
      • Normal Condition: Check if the sample size is large enough (n ≥ 30) for the Central Limit Theorem to apply.
      • Other Conditions: Check for random sampling, and independence of samples.
  • Hypothesis Test Calculations:
    • Calculate the t-statistic: t = (x̄ – μ) / (s / √n)
    • Determine the degrees of freedom: df = n – 1
    • Find the p-value using the t-statistic and degrees of freedom.
    • Compare the p-value to the significance level (α).

Confidence Interval (Square Footage)

  • Calculate the 95% confidence interval for the mean square footage in the ENC region:
    • Confidence Interval = x̄ ± (t * (s / √n))
    • Find the t-value for a 95% confidence level and df = n – 1.
    • Provide the lower and upper bounds of the confidence interval.

Report Summary

  • Summarize the findings of both hypothesis tests.
  • Provide the range of values for the 95% confidence interval of square footage.
  • Interpret the results in the context of the real estate market.
  • Provide recommendations to the regional sales director based on the analysis.

This question has been answered.

Get Answer
WeCreativez WhatsApp Support
Our customer support team is here to answer your questions. Ask us anything!
👋 Hi, Welcome to Compliant Papers.
Hi, how can I help?