Question

A realtor studies the relationship between the size of a house (in square feet) and the property taxes (in $) owed by the owner. The table below shows a portion of the data for 20 homes in a suburb 60 miles outside of New York City. [You may find it useful to reference the t table.]

Property Taxes	Size
21892	2498
17421	2419
18170	1877
15679	1011
43962	5607
33657	2575
15300	2248
16789	1984
18108	2021
16794	1311
15113	1327
36069	3033
31058	2871
42126	3346
14392	1533
38911	4032
25323	4041
22972	2446
16160	3596
29215	2871

a-1. Calculate the sample correlation coefficient r_xy. (Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)

a-2. Interpret r_xy.

a. The correlation coefficient indicates a positive linear relationship.

b. The correlation coefficient indicates a negative linear relationship.

c. The correlation coefficient indicates no linear relationship.

b. Specify the competing hypotheses in order to determine whether the population correlation coefficient between the size of a house and property taxes differs from zero.

a. H₀: ρ_xy = 0; H_A: ρ_xy ≠ 0

b. H₀: ρ_xy ≥ 0; H_A: ρ_xy < 0

c. H₀: ρ_xy ≤ 0; H_A: ρ_xy > 0

c-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

c-2. Find the p-value.

a. p-value < 0.01

b. p-value  0.10

c. 0.05  p-value < 0.10

d. 0.02  p-value < 0.05

e. 0.01  p-value < 0.02

d. At the 5% significance level, what is the conclusion to the test?

a. Reject H₀; we can state size and property taxes are correlated.

b. Reject H₀; we cannot state size and property taxes are correlated.

c. Do not reject H₀; we can state size and property taxes are correlated.

d. Do not reject H₀; we cannot state size and property taxes are correlated.

Answer 1

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