Question

Neighborhood homeowners association suspects that the recent appraisal values of the houses in the neighborhood conducted by the county government for taxation purposes is too high. It hired a private company to appraise the values of a random sample of ten houses in the neighborhood. The results in thousands of dollars are:

House	County government	Private Company
1	217	219
2	350	338
3	296	291
4	237	237
5	237	235
6	272	269
7	257	239
8	277	275
9	312	320
10	335	335

Blank #1:  Samples are matched because they are paired by same __________.

Blank #2: Give a point estimate for the difference in the mean government appraisal of all homes and the mean private appraisal of all homes.  Report your answer with two decimals. Call government 1 and private 2 in proceeding with analysis.  

The 99% confidence interval for the difference, using these data is (-04.271, 10.671)  Because the confidence interval includes 0, we must believe that the mean appraisal values are blank #3?

Perform the relevant test at a significance level of 1% and fill in the following blanks.

Use the framework below to guide your work.

Blank #4: Fill in the alternative hypothesis with the correction notation (<, > or not equals)

H0:  μd=0HA:  μd______________0

Blank #5: Test statistic = _________ (round to two decimal places)

Blank #6:  p-value = __________ (round to four decimal places)

Blank #7: Test decision: We decide to ___________ Ho (reject or do not reject)

Blank #8: Conclusion back into the words of problem: The evidence __________(favors or does not favor) that the mean appraisal value from the county government is higher than that of the mean appraisal value from the private company.

Answer 1

1) Samples are matched because they are paired by same samples.

2) = (-2 + 12 + 5 + 0 + 2 + 3 + 18 + 2 + (-8) + 0)/10 = 3.20

s_d = sqrt(((-2 - 3.2)^2 + (12 - 3.2)^2 + (5 - 3.2)^2 + (0 - 3.2)^2 + (2 - 3.2)^2 + (3 - 3.2)^2 + (18 - 3.2)^2 + (2 - 3.2)^2 + (-8 - 3.2)^2 + (0 - 3.2)^2)/9) = 7.2694

The point estimate for difference in mean = = 3.20

3) Because the confidence interval includes 0, we must believe that the mean appraisal values are equal.

4)

  

5) The test statistic is

  

  

6) df = 10 - 1 = 9

P-value = P(T > 1.39)

= 1 - P(T < 1.39)

= 1 - 0.9010

= 0.0990

7) Since the P-value is greater than the significance level (0.0990 > 0.01), so we should not reject the null hypothesis.

The evidence does not favor that the mean appraisal value from the country government is higher than that of the mean appraisal value from the private company.