Question

An appraiser is appraising an office building in Manhattan. Assume that the population of these appraisals is normally distributed. For commercial appraisals, a comparison analysis and a cost analysis is done. A comparison analysis involves finding the sale prices of several comparable properties (within the last six months) and computing an average value. The cost method involves determining the present cost of duplicating the given property. Clearly, if the comparable analysis yields a present market price greater than the cost of duplicating the given property, the price is not a good deal to an investor, and vice versa. Using the comparison analysis method, the appraiser collected sales data on nine comparable buildings, yielding values of $111,520,000, $112,460,000, $111,940,000, $112,601,000, $110,980,000, $111,200,000, $112,750,000, $112,400,000, and $111,680,000. Using the cost approach, the appraisal was $112,525,000. At the 5% level of significance, should the appraiser conclude that the two appraisals are the same or different?

Step 1 of 4: Consider the problem scenario. The mean of the comparable properties is $111,948,000. What are the logical hypotheses? Use a significance level of 5%.

A) H₀: μ  ≤  $112,525,000 H_a: μ > $112,525,000

B) H₀: μ = $112,525,000 H_a: μ ≠ $112,525,000

C) H₀: μ ≠ $112,525,000 H_a: μ = $112,525,000

D) H₀: μ ≥  $112,525,000 H_a: μ <  $112,525,000

Step 2 of 4: What is the classical approach decision rule for the null hypothesis?

A) If | t |  <  1.860, reject the null hypothesis.

B) If t  >  1.860, reject the null hypothesis.

C) If t  <  -1.860, reject the null hypothesis.

D) If | t |  >  1.860, reject the null hypothesis.

Step 3 of 4: Using the classical approach, state the conclusion of the test.

A) It is a certainty that the comparison appraisal is less than the cost appraisal.

B) At the 5% level, fail to reject the null hypothesis; there is not sufficient sample evidence to claim that the comparison appraisal is less than the cost appraisal.

C) At the 5% level, reject the null hypothesis; there is sufficient sample evidence to conclude that the comparison appraisal is less than the comparison appraisal is less than the cost appraisal.

D) At the 5% level, the results are inconclusive.

Step 4 of 4: Using the p-value approach, state the conclusion of the test.

A) Since the p-value of 0.000 is less than the stated significance level of 0.05, the test is inconclusive.

B) Since the p-value of 0.100 is not less than the stated significance level of 0.05, fail to reject the null hypothesis

C) Since the p-value of 0.027 is less than the stated significance level of 0.05, fail to reject the null hypothesis

D) Since the p-value of 0.014 is less than the stated significance level of 0.05, reject the null hypothesis

Answer 1

Answer)

1)

Ho : u = 112525000

Ha : u < 112525000

2)

As the population s.d is unknown we will use t table to estimate the critical value

Degrees of freedom = n-1, 9-1, 8

For df 8 and alpha 0.05 (5%)

Critical value from t table is -1.86

If t is <-1.86 reject the null hypothesis (option c)

3)

First we need to find the test statistics

So, to find the test statistics we need to determine the mean and s.d

Mean is = 111947888.8889

S.d = 641059.7563

Test statistics = (mean - claimed mean)/(s.d/√n)

N = 9

After substitution

Test statistics t = -2.7

As -2.7 is less than -1.86

Reject the null hypothesis

At the 5% level, reject the null hypothesis; there is sufficient sample evidence to conclude that the comparison appraisal is less than the comparison appraisal is less than the cost appraisal

4)

For 8 df and -2.7 test statistics

P-value from t table is = 0.014

Since the p-value of 0.014 is less than the stated significance level of 0.05, reject the null hypothesis