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...

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.]

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.

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

• 
  
  
  

  
  H
  ₀:
  ρ_xy
  
  = 0;
  H
  _A:
  ρ_xy
  
  ≠ 0

  
  
  
  


• 
  
  
  

  
  H
  ₀:
  ρ_xy
  
  ≥ 0;
  H
  _A:
  ρ_xy
  
  <>

  
  
  
  


• 
  
  
  

  
  H
  ₀:
  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.

multiple choice 3

• 
  
  
  

  
  p-value <>

  
  
  
  


• 
  
  
  

  
  p-value > and equal to 0.10

  
  
  
  


• 
  
  
  

  0.05 < and="" equal="">
  p-value <>

  
  
  
  


• 
  
  
  

  0.02 < and="" equal="">
  p-value <>

  
  
  
  

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

multiple choice 4

• 
  
  
  

  Reject
  H
  ₀; we can state size and property taxes are correlated.

  
  
  
  


• 
  
  
  

  Reject
  H
  ₀; we cannot state size and property taxes are correlated.

  
  
  
  


• 
  
  
  

  Do not reject
  H
  ₀; we can state size and property taxes are correlated.

  
  
  
  


• 
  
  
  

  Do not reject
  H
  ₀; we cannot state size and property taxes are correlated.

  
  

  
  
  
  

Extracted text: Property Taxes Size 21884 2464 17478 2450 18134 1893 15668 1061 43986 5605 33668 2572 15244 2229 16707 1954 18131 2075 16752 1390 15150 1393 36066 3064 31096 2896 42131 3347 14382 1538 38943 4092 25344 4092 22992 2485 16179 3590 29235 2846