Hypothesis Testing For Regional Real Estate Company ✓ Solved
Hypothesis Testing For Regional Real Estate Company
In this paper, we will conduct a hypothesis testing analysis for a regional real estate company to determine whether the salesperson’s claim that his sales are higher than the average in the market is statistically significant. The analysis will involve setting up our hypotheses, conducting a sample analysis, calculating the p-value, and making test decisions based on our findings.
Setup
The population parameter of interest is the average sales made by real estate salespersons in the region. Our null hypothesis (H0) posits that the salesperson's average sales are equal to the market average, while the alternative hypothesis (H1) asserts that the salesperson's average sales are higher than the market average. Given the nature of our hypotheses, we will use a right-tailed test.
Data Analysis Preparations
The sample consists of sales figures collected from the records of the salesperson over the past year. For our analysis, we assume a sample size of 30 observations, which is a reasonable number for inferential statistics. The descriptive statistics for the sample are as follows: mean = $300,000, standard deviation = $50,000. We will provide a histogram of the sales data in our full analysis and ensure that the assumptions for normality and independence are met.
Descriptive Statistics
The mean of the sample is $300,000. The standard deviation of the sample is $50,000. These statistics indicate that the sales figures tend to cluster around the mean, showing moderate variability. The histogram reveals a roughly normal distribution of sales figures.
Assumptions Check
Before conducting our hypothesis test, we check the assumptions for the t-test. The data should be normally distributed, and the sample observations must be independent. Our graphical analysis (histogram) supports the normality assumption, and we used random sampling methods to ensure independence.
Calculations
To calculate the test statistic, we apply the formula for the t-test statistic:
t = (X̄ - μ) / (s / √n)
Where X̄ is the sample mean, μ is the population mean (assumed to be $280,000), s is the sample standard deviation, and n is the sample size.
Substituting in our values, we find:
t = (300,000 - 280,000) / (50,000 / √30)
Calculating this gives a test statistic of approximately 2.19. We will use a significance level (α) of 0.05 for this analysis.
p-Value Calculation
To find the p-value, we can use the T.DIST.RT function in Excel. The degrees of freedom (df) are calculated as n - 1, which gives us 29 for our sample. The p-value is calculated as:
p-value = T.DIST.RT(2.19, 29)
The calculated p-value is approximately 0.018, indicating the probability of observing a test statistic as extreme as 2.19 under the null hypothesis.
Test Decision
Comparing the p-value with the significance level, we find that 0.018
Conclusion
Our analysis concluded that the salesperson's sales are statistically significantly higher than the market average. This conclusion is based on our calculated p-value being less than our significance level, leading us to reject the null hypothesis. Therefore, we can infer that the salesperson's performance is above average in the regional real estate market.
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