Question

1. A mathematics professor wants to determine whether there is a difference in the final averages between the past two semesters (semester I and semester II) of his business statistics classes. For a random sample of 16 students from semester I, the mean of the final averages was 75 with a standard deviation of 4. For a random sample of 9 students from semester II, the mean was 73 with a standard deviation of 6.

If the final averages from semesters I and II are assumed to be normally distributed with equal variances, the correct decision for the appropriate test at a 0.05 level of significance when the population variances are assumed to be equal is

a) reject the alternative hypothesis.
b) reject the null hypothesis.
c) do not reject the null hypothesis.
d) do not reject the alternative hypothesis.

1. 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%.

H₀: μ  ≤ $112,525,000       H_a: μ > $112,525,000
H₀: μ = $112,525,000       H_a: μ ≠ $112,525,000
H₀: μ ≠ $112,525,000       H_a: μ = $112,525,000
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