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

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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
  21,872     2,464  
  17,498     2,451  
       
  29,294     2,895  
 

 

 

 

 Click here for the Excel Data File

 

 

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

 

 

 

 

a-2. Interpret rxy.

 

multiple choice 1

  • The correlation coefficient indicates a positive linear relationship.
  • The correlation coefficient indicates a negative linear relationship.
  • 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. 

 

multiple choice 2

  • H0ρxy = 0; HAρxy ≠ 0
  • H0ρxy ≥ 0; HAρxy < 0
  • H0ρxy ≤ 0; HAρxy > 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.

 

multiple choice 3

  • p-value < 0.01
  • p-value 
     
     0.10
     
  • 0.05 
     
     p-value < 0.10
     
  • 0.02 
     
     p-value < 0.05
     
  • 0.01 
     
     p-value < 0.02
     

 

 

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

 

multiple choice 4

  • Reject H0; we can state size and property taxes are correlated.
  • Reject H0; we cannot state size and property taxes are correlated.
  • Do not reject H0; we can state size and property taxes are correlated.
  • Do not reject H0; we cannot state size and property taxes are correlated.

 

 

A
В
Property Taxes
Size
21872
2464
17498
2451
18187
1845
15663
1070
43971
5651
33633
2555
15246
2265
16742
1937
18155
2039
16769
1307
15132
1325
36007
3093
31033
2883
42179
3324
14386
1594
38935
4031
25328
4036
22928
2485
16114
3503
29294
2895
Transcribed Image Text:A В Property Taxes Size 21872 2464 17498 2451 18187 1845 15663 1070 43971 5651 33633 2555 15246 2265 16742 1937 18155 2039 16769 1307 15132 1325 36007 3093 31033 2883 42179 3324 14386 1594 38935 4031 25328 4036 22928 2485 16114 3503 29294 2895
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