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 alternative hypothesis HA ?

A.     HO :  ρ > 0   HA :  ρ = 0

B.   HO :  ρ = 0   HA :  ρ > 0

C.   HO :  ρ = 0   HA :  ρ < 0

D.     none of these answers are correct

(ii) Enter the level of significance α 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

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(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

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(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

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(vi) Comparing p-value and α 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

Answer 1

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 alternative hypothesis HA ?

B. HO : ρ = 0 HA : ρ > 0

(ii) Enter the level of significance α used for this test, and the degrees of freedom df:

0.05, 46

(iii) Use technology to determine correlation coefficient r between independent variable (house value) and dependent variable (annual rental income)

0.7647

(iv) Calculate and enter test statistic
8.0487

(v) Using tables, calculator, or spreadsheet: Determine and enter p-value corresponding to test statistic.
0.000   

(vi) Comparing p-value and α value, which is the correct decision to make for this hypothesis test?

A. Reject Ho

(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.

Detailed calculation given below

Put the values in excel as shown use the formulas.