A real estate agent wishes to determine whether a tax assessors and real estate appraises agree on the values of homes. A random sample of the two groups appraised 10 homes. The data are shown here. Is there a significant difference in the values of the homes for each group? Let alpha = 0.05. Use p value method.
Sample mean 
Real estate appraiser $83,256 
tax assessors $88,354 

s1= $3256  s2= 2341  
N1= 10  n2= 10 
From the given information, the claim of the problem is there is a significance difference in the values of homes for real estate appraises and tax assessors.
Let us define µ_{1} be the population mean for real estate appraises and µ_{2} be the population mean for tax assessors.
Null hypothesis:
H_{0}: µ_{1}= µ_{2}.
That is, there is no significance difference in the values of homes for real estate appraises and tax assessors.
Alternative hypothesis:
H_{1}: µ_{1}≠µ_{2}.
That is, there is a significance difference in the values of homes for real estate appraises and tax assessors.
From the given information, the sample mean for real estate appraises is $83,256, the sample mean for tax assessors is $88,354 , the sample standard deviation for real estate appraises is s1= 3256, the sample standard deviation for tax assessors is s2= 2341. The sample size for real estate appraises is n_{1}=10 and the sample size for tax assessors is n_{2}=10.
Here, the population standard deviations are unknown and the sample sizes are less than 30. Moreover, the two samples are independent. Hence, the suitable test for testing the given hypothesis is twosample independent t test.
The test statistic is 4.02 and it is calculated below:
The pvalue is 0.0008 and it is calculated below:
The degrees of freedom is n1+n2...
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