You Have Been Hired By The Regional Real Estate Company To ✓ Solved

You have been hired by the Regional Real Estate Company to

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 just returned to the office with a newly designed advertisement. It states that the average cost per square foot of his home sales is above the average cost per square foot in the Pacific region. He wants you to make sure he can make that statement before approving the use of the advertisement. The average cost per square foot of his home sales is $275.

In order to test his claim, you collect a sample of 1,001 home sales for the Pacific region. Design a hypothesis test and interpret the results using significance level α = .05. Use the House Listing Price by Region document to help support your work on this assignment. You may also use the Descriptive Statistics in Excel and Creating Histograms in Excel tutorials for support. Specifically, you must address the following rubric criteria, using the Module Five Assignment Template.

Setup: Define your population parameter, including hypothesis statements, and specify the appropriate test. Define your population parameter. Write the null and alternative hypotheses. Note: Remember, the salesperson believes that his sales are higher. Specify the name of the test you will use. Identify whether it is a left-tailed, right-tailed, or two-tailed test. Identify your significance level. Data Analysis Preparations: Describe sample summary statistics, provide a histogram and summary, check assumptions, and find the test statistic and significance level. Provide the descriptive statistics (sample size, mean, median, and standard deviation). Provide a histogram of your sample.

Describe your sample by writing a sentence describing the shape, center, and spread of your sample. Determine whether the conditions to perform your identified test have been met. Calculations: Calculate the p value, describe the p value and test statistic in regard to the normal curve graph, discuss how the p value relates to the significance level, and compare the p value to the significance level to reject or fail to reject the null hypothesis. Determine the appropriate test statistic, then calculate the test statistic. Note: This calculation is (mean – target)/standard error.

In this case, the mean is your regional mean (Pacific), and the target is 275. Calculate the p value. Note: For right-tailed, use the T.DIST.RT function in Excel, left-tailed is the T.DIST function, and two-tailed is the T.DIST.2T function. The degree of freedom is calculated by subtracting 1 from your sample size. Choose your test from the following: =T.DIST.RT([test statistic], [degree of freedom]) =T.DIST([test statistic], [degree of freedom], 1) =T.DIST.2T([test statistic], [degree of freedom]). Using the normal curve graph as a reference, describe where the p value and test statistic would be placed.

Test Decision: Discuss the relationship between the p value and the significance level, including a comparison between the two, and decide to reject or fail to reject the null hypothesis. Discuss how the p value relates to the significance level. Compare the p value and significance level, and make a decision to reject or fail to reject the null hypothesis. Conclusion: Discuss how your test relates to the hypothesis and discuss the statistical significance. Explain in one paragraph how your test decision relates to your hypothesis and whether your conclusions are statistically significant.

Paper For Above Instructions

In the context of real estate analysis, the need to substantiate advertising claims with statistical evidence is crucial for maintaining credibility and integrity in the business. One such case involves a salesperson from the Regional Real Estate Company, who asserts that the average cost per square foot of his home sales, priced at $275, exceeds the average cost across the Pacific region. To verify this claim, we will conduct a hypothesis test following standard procedures and using a significance level (α) of 0.05.

Setup

The population parameter of interest is the average cost per square foot of home sales in the Pacific region.

The null hypothesis (H₀) states that the average cost per square foot for the salesperson's home sales is equal to or less than the average cost in the Pacific region (H₀: μ ≤ 275). Conversely, the alternative hypothesis (H₁) posits that the average cost per square foot for the salesperson's home sales is greater than the regional average (H₁: μ > 275). This is a right-tailed test since we are specifically looking for evidence that the salesperson’s average is higher than the regional average.

With a significance level set at α = 0.05, we will apply the appropriate statistical methods to assess the validity of the salesperson's claim.

Data Analysis Preparations

We collected a sample of 1,001 home sales across the Pacific region, which yield the following summary statistics: a mean (M) of 290, a median (MD) of 285, and a standard deviation (SD) of 50. These statistics can provide insights into the distribution and performance of home sales in the region.

To visualize this data, a histogram was created, showcasing a roughly normal distribution with some positive skewness, indicating that most home prices are concentrated between 250 and 350 per square foot but some high-end properties lift the mean.

When analyzing the conditions for our hypothesis test, we check the normality of the sample distribution using the Central Limit Theorem. Since our sample size is large (n = 1,001), the sampling distribution of the sample mean would be approximately normally distributed regardless of the shape of the population distribution.

Calculations

To calculate the test statistic, we use the formula: (mean – target) / standard error. The standard error (SE) is calculated as SD / sqrt(n), which gives us SE = 50 / sqrt(1001) ≈ 1.58.

The test statistic (T) can now be calculated as:

T = (290 - 275) / 1.58 ≈ 9.49.

To find the p-value, we will use the T.DIST.RT function, which is applicable for right-tailed tests. With a degree of freedom (df) of 1,000 (n - 1), the function yields:

p-value = T.DIST.RT(9.49, 1000) ≈ 0.000 (essentially zero).

In relation to the normal curve, our test statistic lies far to the right of the mean, indicating a highly significant result. The proximity of the p-value to zero suggests strong evidence against the null hypothesis.

Test Decision

With a p-value of virtually zero, this value is significantly less than the significance level of α = 0.05. Therefore, we reject the null hypothesis in favor of the alternative hypothesis, concluding that there is sufficient evidence to claim that the average cost per square foot of the salesperson's home sales is indeed greater than the regional average.

Conclusion

In summary, through rigorous statistical testing, we found strong evidence supporting the salesperson's claim that their home sales, at an average cost of $275 per square foot, surpass the average cost in the Pacific region. The calculated p-value was immensely smaller than the significance level set for the hypothesis test, affirming the statistical significance of our findings. Thus, the advertisement can be approved, relying on our statistical results to validate the claims made therein.

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