The table below contains the value of the house and the amount of rental income
ID: 2946631 • Letter: T
Question
The table below contains the value of the house and the amount of rental income in a year that the house brings in ("Capital and rental," 2013).
Table: Data of House Value versus Rental
Value
Rental
Value
Rental
Value
Rental
Value
Rental
81000
6656
77000
4576
75000
7280
67500
6864
95000
7904
94000
8736
90000
6240
85000
7072
121000
12064
115000
7904
110000
7072
104000
7904
135000
8320
130000
9776
126000
6240
125000
7904
145000
8320
140000
9568
140000
9152
135000
7488
165000
13312
165000
8528
155000
7488
148000
8320
178000
11856
174000
10400
170000
9568
170000
12688
200000
12272
200000
10608
194000
11232
190000
8320
214000
8528
208000
10400
200000
10400
200000
8320
240000
10192
240000
12064
240000
11648
225000
12480
289000
11648
270000
12896
262000
10192
244500
11232
325000
12480
310000
12480
303000
12272
300000
12480
Test at the 5% level for a positive correlation between house value and rental amount.
(i) Which of the following statements correctly define both the null hypothesis HO and the alternate hypothesis HA ?
A. HO : ? > 0 HA : ? = 0
B. HO : ? = 0 HA : ? > 0
C. HO : ? = 0 HA : ? < 0
D. none of these answers are correct
(ii) Enter the level of significance ? used for this test, and the degrees of freedom df:
Enter level of significance in decimal form to nearest hundredth, followed by comma, followed by degrees of freedom value to nearest integer. Do not enter spaces.
Examples of correctly entered answers: 0.01,4 0.02,11 0.05,13 0.10,46
(iii) Use technology to determine correlation coefficient r between independent variable (house value) and dependent variable (annual rental income)
Enter in decimal form to nearest ten-thousandth with sign (positive or negative). Examples of correctly entered answers:
-0.0001 +0.0020 -0.0500 +0.3000 +0.7115
Recommended online calculator:
Correlation and Linear Regression Calculator Applet
(iv) Calculate and enter test statistic
Enter value in decimal form rounded to nearest hundredth, with appropriate sign (no spaces). Examples of correctly entered answers:
–2.10 –0.07 +0.60 +1.09
Recommended online calculators:
Correlation Coefficient - Testing Significance
(v) Using tables, calculator, or spreadsheet: Determine and enter p-value corresponding to test statistic.
Enter value in decimal form rounded to nearest thousandth. Examples of correctly entered answers:
0.000 0.001 0.030 0.600 0.814 1.000
Recommended online calculator:
Correlation Coefficient - Testing Significance
(vi) Comparing p-value and ? value, which is the correct decision to make for this hypothesis test?
A. Reject Ho
B. Fail to reject Ho
C. Accept Ho
D. Accept HA
Enter letter corresponding to correct answer.
(vii) Select the statement that most correctly interprets the result of this test:
A. The result is statistically significant at .05 level of significance. Evidence supports the claim that there is a positive correlation between house value and rental amount.
B. The result is statistically significant at .05 level of significance. There is not enough evidence to show that there is a positive correlation between house value and rental amount.
C. The result is not statistically significant at .05 level of significance. Evidence supports the claim that there is a positive correlation between house value and rental amount.
D. The result is not statistically significant at .05 level of significance. There is not enough evidence to show that there is a positive correlation between house value and rental amount.
Enter letter corresponding to most correct answer
Value
Rental
Value
Rental
Value
Rental
Value
Rental
81000
6656
77000
4576
75000
7280
67500
6864
95000
7904
94000
8736
90000
6240
85000
7072
121000
12064
115000
7904
110000
7072
104000
7904
135000
8320
130000
9776
126000
6240
125000
7904
145000
8320
140000
9568
140000
9152
135000
7488
165000
13312
165000
8528
155000
7488
148000
8320
178000
11856
174000
10400
170000
9568
170000
12688
200000
12272
200000
10608
194000
11232
190000
8320
214000
8528
208000
10400
200000
10400
200000
8320
240000
10192
240000
12064
240000
11648
225000
12480
289000
11648
270000
12896
262000
10192
244500
11232
325000
12480
310000
12480
303000
12272
300000
12480
Explanation / Answer
(i) Correct answer: Option (B)
ii) 0.05,42
iii) Correlation coefficient : 0.7647
The regresion equation is
Rental = 5363.864821 +0.024358242 Value
iv) Test Statistic t = 8.0496,
v) P-value = 0.0000
vi) Correct answer: Option (B)
vii) Option (A). The result is statistically significant at .05 level of significance. Evidence supports the claim that there is a positive correlation between house value and rental amount.
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