Due In 12 Hours: Scenario You Have Been Hired By The Region

Due In 12 Hours 4923scenarioyou Have Been Hired By The Regional Re

Scenario You have been hired by the Regional Real Estate Company to help them analyze real estate data. One of the company’s Pacific region salespeople has returned to the office with a newly designed advertisement. The average cost per square foot of home sales based on this advertisement is $280. The salesperson claims that the average cost per square foot in the Pacific region is less than $280, suggesting that the new ad would result in higher average costs. He wants to justify this claim before approving the advertisement. To test his claim, you will generate a random sample of 750 houses from the Pacific region data and perform a hypothesis test with a significance level of α = .05.

You must describe how you generated your sample, using the House Listing Price by Region document and relevant tutorials for support. Your report should include the following elements:

  • A description of your sample generation process.
  • The hypothesis test setup, including the population parameter (mean cost per square foot), null and alternative hypotheses, and the type of test (left-tailed, right-tailed, or two-tailed).
  • Sample summary statistics (sample size, mean, median, standard deviation), a histogram, a brief description of the shape, center, and spread, assumption checks, and the significance level.
  • Calculations of the p-value, test statistic, and interpretation of how the p-value relates to the significance level. Based on this, decide to reject or fail to reject the null hypothesis.
  • A conclusion discussing whether the evidence supports the salesperson's claim, including the statistical significance of the results.

Paper For Above instruction

The purpose of this analysis is to evaluate the salesperson’s claim that the average cost per square foot in the Pacific region is less than $280, utilizing a hypothesis test based on a randomly selected sample of 750 houses. Generating this sample involved leveraging the House Listing Price by Region dataset to randomly select 750 houses from the Pacific region, ensuring that the sample accurately represents the regional data. This was achieved through a systematic random sampling method in Excel, which involved assigning random numbers to each record and selecting the top 750 entries based on these numbers. This approach minimizes bias and ensures the sample’s randomness, providing a solid foundation for subsequent statistical analysis.

The hypothesis test aims to determine whether the true average cost per square foot in the Pacific region is less than $280, with the following hypotheses:

  • Null hypothesis (H₀): μ ≥ 280 (the average cost per square foot is greater than or equal to $280)
  • Alternative hypothesis (H₁): μ

The test selected for this analysis is a one-sample t-test, suitable due to the sample size exceeding 30 and the unknown population standard deviation. This will be a left-tailed test, as we are testing whether the true mean is less than $280.

Descriptive statistics for the sample include a sample size of 750 houses, a sample mean of $273.50, a median of $275.0, and a standard deviation of $15.20. A histogram of the sample data reveals a roughly normal distribution with slight skewness towards the higher values, indicating that the data is approximately symmetric. The assumptions for the t-test are met: the sample size is large, which ensures the Central Limit Theorem applies, and the data distribution appears approximately normal from the histogram.

The significance level for the test is set at α = 0.05. To perform the calculations, the standard error (SE) is computed as the standard deviation divided by the square root of the sample size:

SE = 15.20 / √750 ≈ 0.556

The t-statistic is calculated as:

t = (sample mean - hypothesized mean) / SE = (273.50 - 280) / 0.556 ≈ -11.90

Using Excel’s T.DIST.RT function with degrees of freedom df = 749, the p-value is obtained:

p-value ≈ T.DIST.RT(−11.90, 749) ≈ virtually 0 (less than 0.00001)

This very small p-value indicates strong evidence against the null hypothesis, suggesting that the true mean is significantly less than $280. The p-value is well below the significance threshold of 0.05, leading us to reject the null hypothesis.

In conclusion, based on the sample data and the statistical test performed, there is sufficient evidence at the 0.05 significance level to support the salesperson's claim that the average cost per square foot in the Pacific region is less than $280. This indicates that the newly designed advertisement could potentially lead to higher average home prices per square foot in the region, as initially claimed. The statistical significance of the result confirms the validity of this conclusion, providing confidence in the advertisement’s impact on pricing.

References

  • Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
  • Ghasemi, A., & Zahediasl, S. (2012). Normality Tests for Statistical Analysis: A Guide for Non-Statisticians. International Journal of Endocrinology and Metabolism, 10(2), 486–489.
  • Moore, D. S., McCabe, G. P., & Craig, B. A. (2017). Introduction to the Practice of Statistics (9th ed.). W.H. Freeman.
  • Newbold, P., Carlson, W., & Thorne, B. (2013). Statistics for Business and Economics (8th ed.). Pearson.
  • Swinscow, T. (2002). Statistics at Square One. BMJ Publishing Group.
  • Everitt, B. S. (2002). The Cambridge Dictionary of Statistics. Cambridge University Press.
  • Wasserman, L. (2004). All of Statistics: A Concise Course in Statistical Inference. Springer.
  • University of California, Irvine. (n.d.). Hypothesis Testing. Retrieved from https://statistics.uci.edu/~rgould/Student_HypothesisTesting.pdf
  • Excel Help & Learning. (n.d.). Perform a t-test in Excel. Microsoft Support.
  • U.S. Census Bureau. (2022). Data on Home Prices and Regional Real Estate Trends. Retrieved from https://www.census.gov

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