Question

A real estate agent wishes to determine whether tax assessors and real estate appraisers agree on the vales of homes. A random sample of the two groups appraised 10 homes. The mean and standard deviations are shown below. Is there a significant difference in the values of the homes for each group? Let α=0.05. Test the hypothesis that the two appraisers differ in their appraisal values of the 10 homes. Solve using the traditional method. Data is also available in SPSS, HW6Q3.sav . Include the SPSS output you used to solve this problem. tax assessors: 87,800 std deviation: 6795.423 n= 10 Real estate: 83,400 std deviation: 5541.761 n= 10

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u₁ = u ₂
Alternative hypothesis: u₁ u₂

Note that these hypotheses constitute a two-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = sqrt[(s₁²/n₁) + (s₂²/n₂)]
SE = 2772.885
DF = 18
t = [ (x₁ - x₂) - d ] / SE

t = 1.59

where s₁ is the standard deviation of sample 1, s₂ is the standard deviation of sample 2, n₁ is the size of sample 1, n₂ is the size of sample 2, x₁ is the mean of sample 1, x₂ is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.

Since we have a two-tailed test, the P-value is the probability that a t statistic having 18 degrees of freedom is more extreme than -1.59; that is, less than -1.59 or greater than 1.59.

Thus, the P-value = 0.065

Interpret results. Since the P-value (0.065) is greater than the significance level (0.05), hence we failed to reject null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that the two appraisers differ in their appraisal values of the 10 homes.