A small independent organic food store offers a variety of specialty coffees. To
ID: 3208597 • Letter: A
Question
A small independent organic food store offers a variety of specialty coffees. To determine whether price has an impact on sales, the managers kept track of how many pounds of each variety of coffee were sold last month. The data, scatterplot, and summary statistics are shown below.
Price (lb)
Pounds Sold
3.99
75
5.99
6
7.00
65
12.00
45
9.50
80
7.50
70
15.00
25
10.00
35
12.50
40
8.99
50
Mean
8.75
54.50
Standard Deviation
3.63
18.33
Correlation
-0.927
The linear relationship between number of pounds of coffee sold per week and price is best described as
Select one:
a. strong and positive.
b. nonexistent.
c. weak and positive.
d. weak and negative.
e. strong and negative.
Price (lb)
Pounds Sold
3.99
75
5.99
6
7.00
65
12.00
45
9.50
80
7.50
70
15.00
25
10.00
35
12.50
40
8.99
50
Mean
8.75
54.50
Standard Deviation
3.63
18.33
Correlation
-0.927
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 /10 (4289.69) - [ 1/10 *92.47 ] [ 1/10 *491] = -25.059
S. D ( X ) = Sqrt( 1/10*953.3703-(1/10*92.47)^2) = 3.135
S .D (Y) = Sqrt( 1/10*29161-(1/10*491)^2) = 22.479
r(x,y) = -25.059 / 3.135*22.479 = -0.3556
If r = -0.3556< 0, Negative Correlation
[ANSWER]
d. weak and negative.
( X) ( Y) X^2 Y^2 X*Y 3.99 75 15.9201 5625 299.25 5.99 6 35.8801 36 35.94 7 65 49 4225 455 12 45 144 2025 540 9.5 80 90.25 6400 760 7.5 70 56.25 4900 525 15 25 225 625 375 10 35 100 1225 350 12.5 40 156.25 1600 500 8.99 50 80.8201 2500 449.5 92.47 491 953.3703 29161 4289.69 = TOTALSRelated Questions
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