In the town of Lexington, Massachusetts, the real estate company VALMAX has received many complaints from two sets of customers: the first set believes that they were advised to post asking-prices for their houses that were too low compared to other brokers’ listings while the second set believes that they were advised to accept selling-prices for houses that they purchased that were too high relative to the selling-prices for houses brokered by other realtors. Based on the given data for both VALMAX and the other brokers (will henceforth be called “OTHERS”), it is decided that the clients’ complaints are justified.
In order to properly come up with this conclusion, the ...view middle of the document...
When combined, they are cumulatively complaining that the difference between the asking and selling price is too low. Therefore, the null hypothesis states that VALMAX’s difference is greater than or equal to the OTHERS difference. This indicates that VALMAX is not at fault and is not cheating their clients. The alternative hypothesis states that VALMAX’s difference is less than OTHERS difference and is therefore at fault and their clients’ complaints are justified (Exhibit 1).
Degrees of Freedom and Defined Rejection Region:
To calculate the degrees of freedom, the number of samples taken from VALMAX is added to the number of samples taken from OTHERS and then the number 2 is subtracted. This calculates to 77. Because this number is greater than or equal to 30, we use the z table to define the rejection region. Using an alpha of 0.05 (confidence level of 95%), the z value comes out to -1.645. Our alternative hypothesis states that we are looking at a left-sided, one-tailed rejection area (Exhibit 2).
Calculating and Interpreting the Test Statistic:
The average and standard deviation are first calculated on Excel for both VALMAX and OTHERS. Using the formula for the hypothesis test for two means, the test statistic is calculated out as -2.0604 (Exhibit 3). As mentioned earlier, there are three ways to now come up with a conclusion. The first qualitative way is to draw the normal distribution curves for the differences for both VALMAX and OTHERS and then look at the overlap. In this example, there is very little overlap, so this signifies that the two are not similar and therefore, the differences between them are significant (Exhibit 4). The second method is to compare the test statistic to the z value defining the rejection region. Because the z value is -1.645 and the test statistic is -2.0604, this value falls inside the rejection region and we can conclude that we have enough information to reject the null hypothesis and therefore, accept the alternative hypothesis. The third method is to compare the p value to alpha. The p value is determined by using the test statistic to find the...