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Assignment Solution Presentation: Hypothesis Testing for Housing Prices and Square Footage in East South Central Region

In this analytical exploration, we delve into the housing market of the East South Central region, employing hypothesis testing to scrutinize two pivotal aspects: housing prices and average square footage. The investigation unfolds with a focused hypothesis that the mean housing price is notably lower than the national average, followed by an exploration of the average square footage, hypothesizing a significant deviation from the national market. Through meticulous 1-Tail and 2-Tail tests, conducted at a 95% confidence level, the findings provide compelling insights into the distinct characteristics of the East South Central housing landscape.

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Problem Description:

The Hypothesis Testing Assignment focuses on examining two critical parameters related to the housing market in the East South Central region. The first parameter is the mean housing price, with the hypothesis that it is significantly lower than the national marketing average. The second parameter is the average square footage of homes, with the hypothesis that it differs significantly from the national market average. The analysis employs a 1-tail test for housing prices and a 2-tail test for square footage, both conducted at a 95% confidence level.

1-Tail Test for Housing Prices:

Hypotheses:

  • Null Hypothesis (H₀):

    • housing price of East South Central region≥288,407μhousing price of East South Central region≥288,407

  • Alternative Hypothesis (H₁):

    • housing price of East South Central region<288,407μhousing price of East South Central region<288,407

Data Analysis:

  • Sample Mean: $220,023
  • Standard Deviation: $73,475
  • Sample Size (n): 500
  • Confidence Level: 95%
  • Significance Level (α): 0.05

Test Calculations:

  • t-test statistic: -20.81
  • p-value: 0.0000

Interpretation:

  • The p-value (0.0000) is less than the significance level of 0.05.
  • Rejection of the null hypothesis.
  • Conclusion:

    • Housing prices in East South Central are significantly lower than the national marketing average.

2-Tail Test for Square Footage:

Hypotheses:

  • Null Hypothesis (H₀):

    • square footage in East South Central region=288,407μsquare footage in East South Central region=288,407

  • Alternative Hypothesis (H₁):

    • square footage in East South Central region≠288,407μsquare footage in East South Central region=288,407

Data Analysis:

  • Sample Mean: 2,007 sq. ft.
  • Standard Deviation: 329 sq. ft.
  • Sample Size (n): 500
  • Confidence Level: 95%
  • Significance Level (α): 0.05

Test Calculations:

  • t-test statistic: 4.28
  • p-value: 0.0000

Interpretation:

  • The p-value (0.0000) is less than the significance level of 0.05.
  • Rejection of the null hypothesis.
  • Conclusion:

    • The average square footage for homes in East South Central is significantly different from the national market.

Comparison of Test Results:

Housing Prices:

  • 95% Confidence Interval: $213,567.1, $226,478.9
  • Conclusion:

    • Housing prices in East South Central are significantly lower than the national marketing average.

Square Footage:

  • 95% Confidence Interval: 1,978.1,2,035.91,978.1,2,035.9
  • Conclusion:

    • The average square footage for homes in East South Central is significantly different from the national market.

Conclusions:

The statistical analysis leads to the robust conclusion that housing prices in East South Central are significantly lower than the national marketing average. Additionally, the average square footage for homes in East South Central is significantly different from the national market. These findings provide valuable insights into the regional housing market dynamics.