Correlation Coefficient! Question 1 (1 point) The author is a member of the boar

Question

Correlation Coefficient!

Question 1 (1 point) The author is a member of the board of directors of a nonprofit organization that held a fund-raising auction. He recorded the opening bids suggested by the auctioneer and the final winning bids for several items. The amounts are listed below. Answer question 1 and 2 Opening bid 1300500 500A00300 Winning bid 600 195 120 270 125 1. what is the correlation coefficient between the opening bids and the final winning bids? (use the excel templatei keep ecima places o a) o 947 b) 0.878 c) 959 d) 0.935

Explanation / Answer

Correlation

r( X,Y) =Co V ( X,Y) / S.D (X) * S.D (y)                              
r( X,Y) = Sum(XY) / N- Mean of (X) * Mean of (Y) / Sqrt( X^2/n - ( Mean of X)^2 ) Sqrt( Y^2/n - ( Mean of Y)^2 )                                
                              
Co v ( X, Y ) = 1 /5 (1083000) - [ 1/5 *3000 ] [ 1/5 *1310] = 59400                              
S. D ( X ) = Sqrt( 1/5*2440000-(1/5*3000)^2) = 357.771                              
S .D (Y) = Sqrt( 1/5*500950-(1/5*1310)^2) = 177.612                              
r(x,y) = 59400 / 357.771*177.612 = 0.9348                              
                              
If r = 0.9348> 0 ,Perfect Positive Correlation          

PART B.

Given that,
value of r =0.9348
number (n)=5
null, Ho: =0
alternate, H1: !=0
level of significance, = 0.05
from standard normal table, two tailed t /2 =3.182
since our test is two-tailed
reject Ho, if to < -3.182 OR if to > 3.182
we use test statistic (t) = r / sqrt(1-r^2/(n-2))
to=0.9348/(sqrt( ( 1-0.9348^2 )/(5-2) )
to =4.56
|to | =4.56
critical value
the value of |t | at los 0.05% is 3.182
we got |to| =4.56 & | t | =3.182
make decision
hence value of | to | > | t | and here we reject Ho
ANSWERS
---------------
null, Ho: =0
alternate, H1: !=0
test statistic: 4.56
critical value: -3.182 , 3.182
decision: reject Ho

Option A is the answer

( X) ( Y) X^2 Y^2 X*Y 1300 600 1690000 360000 780000 500 195 250000 38025 97500 500 120 250000 14400 60000 400 270 160000 72900 108000 300 125 90000 15625 37500 3000 1310 2440000 500950 1083000 = TOTALS

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