Exercise 14-9 Algo A realtor studies the relationship between the size of a hous

Question

Exercise 14-9 Algo

A realtor studies the relationship between the size of a house (in square feet) and the property taxes owed by the owner. He collects the following data on six homes in an affluent suburb 60 miles outside of New York City. Use Table 2.

Calculate sxy and rxy. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

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

Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

Approximate the p-value.

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

A realtor studies the relationship between the size of a house (in square feet) and the property taxes owed by the owner. He collects the following data on six homes in an affluent suburb 60 miles outside of New York City. Use Table 2.

Explanation / Answer

calculation procedure for correlation
sum of (x) = x = 18702
sum of (y) = y = 63704
sum of (x^2)= x^2 = 66713854
sum of (y^2)= y^2 = 881203240
sum of (x*y)= x*y = 236905576
to caluclate value of r( x,y) = covariance ( x,y ) / sd (x) * sd (y)
covariance ( x,y ) = [ x*y - N *(x/N) * (y/N) ]/n-1
= 236905576 - [ 6 * (18702/6) * (63704/6) ]/6- 1
= 6390034.667
and now to calculate r( x,y) = 6390034.667/ (SQRT(1/6*236905576-(1/6*18702)^2) ) * ( SQRT(1/6*236905576-(1/6*63704)^2)
=6390034.667 / (1184.604*5842.897)
=0.923
value of correlation is =0.923

the scatterplot indicates that there is a positive relationship between size of house and property taxes

covariance ( x,y ) = 6390034.667

rxy = 0.923

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Given that,

value of r =0.923

number (n)=6

null, Ho: =0

alternate, H1: !=0

level of significance, = 0.05

from standard normal table, two tailed t /2 =2.776

since our test is two-tailed

reject Ho, if to < -2.776 OR if to > 2.776

we use test statistic (t) = r / sqrt(1-r^2/(n-2))

to=0.923/(sqrt( ( 1-0.923^2 )/(6-2) )

to =4.8

|to | =4.8

critical value

the value of |t | at los 0.05% is 2.776

we got |to| =4.8 & | t | =2.776

make decision

hence value of | to | > | t | and here we reject Ho

ANSWERS

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H0: xy = 0; HA: xy 0

test statistic: 4.8

critical value: -2.776 , 2.776

decision: reject Ho

P-Value : Two Tailed ( double the one tail ) - Ha = 0.446813

p-value >=0.100

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

( X) ( Y) X^2 Y^2 X*Y 4164 12323 17338896 1.52E+08 51312972 2794 9083 7806436 82500889 25377902 5038 22701 25381444 5.15E+08 114367638 2138 6467 4571044 41822089 13826446 1515 5244 2295225 27499536 7944660 3053 7886 9320809 62188996 24075958

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