MATHEMATICS
1) The following sample observations were randomly selected. 
X : 4 5 3 6 10 Y: 4 6 5 7 7 
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(1)  Fill in the blanks below: (Round your answers to 2 decimal places.) 
correlation between X and Y. 
(3)  Fill in the blanks. (Round your answer to the nearest whole number.) 
The coefficient of determination obtained here indicates X accounts for approximately relationship between X and Y. The coefficient of determination is is the dependent variable. 
(c)  Determine the correlation coefficient. (Round your answer to 2 decimal places.) 
Coefficient of correlation  correlation between the variables. 
4) The production department of Celltronics International wants to explore the relationship between the number of employees who assemble a subassembly and the number produced. As an experiment, two employees were assigned to assemble the subassemblies. They produced 15 during a onehour period. Then four employees assembled them. They produced 25 during a onehour period. The complete set of paired observations follows. 
Number of Assemblers 
OneHour Production (units) 
2  15 
4  25 
1  10 
5  40 
3  30 

The dependent variable is production; that is, it is assumed that different levels of production result from a different number of employees. 
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(b)  A scatter diagram is provided below. Based on it, does there appear to be any relationship between the number of assemblers and production? 
, as the number of assemblers, so does the production. 
(c)  Compute the coefficient of correlation. (Negative amounts should be indicated by a minus sign. Round s_{x}, s_{y} and r to 3 decimal places.) 
X  Y  ( )^{2}  ( )^{2}  ( )( )  
2  15  is the independent variable and is the dependent variable. 
(b1)  Determine the coefficient of correlation. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) 
X  Y  ( )^{2}  ( )^{2}  ( )( )  
9.0  8.1  correlation between age of car and selling price. So, H_{o}. Weconclude that the correlation in the population is greater than zero. 
7) The following hypotheses are given. 
A random sample of 15 paired observations have a correlation of −.46. Can we conclude that the correlation in the population is less than zero? Use the .05 significance level. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) 
Reject H_{0} if t < −1.771  t  =  H_{o}. 
8) The following sample observations were randomly selected. 
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X:  5  3  6  3  4  4  6  8 
Y:  13  15  7  12  13  11  9  5 

(a)  Determine the regression equation. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) 
X  Y  ()^{2}  ()^{2}  ( )( )  
5  13  [removed]  2.375  [removed]  5.641  [removed] 
3  15  −1.875  [removed]  3.516  [removed]  −8.203 
6  7  [removed]  [removed]  [removed]  13.141  −4.078 
3  12  −1.875  1.375  [removed]  [removed]  [removed] 
4  13  −0.875  [removed]  0.766  [removed]  −2.078 
4  11  [removed]  0.375  [removed]  0.141  [removed] 
6  9  1.125  −1.625  [removed]  [removed]  [removed] 
8  5  [removed]  [removed]  [removed]  31.641  −17.578 
[removed]  [removed]  [removed]  [removed]  [removed]  

=  [removed]  =  [removed]  s_{x}  =  [removed] 
s_{y}  =  [removed]  r  =  [removed] 
b  =  [removed]  a  =  [removed] 
Y’ = [removed]+ [removed]X 
(b)  Determine the value of when X is 7. (Round your answer to 3 decimal places.) 
[removed] 
9) Bradford Electric Illuminating Company is studying the relationship between kilowatthours (thousands) used and the number of rooms in a private singlefamily residence. A random sample of 10 homes yielded the following. 
Number of Rooms  KilowattHours (thousands)  Number of Rooms  KilowattHours (thousands)  
12  9  8  6  
9  7  10  8  
14  10  10  10  
6  5  5  4  
10  8  7  7  
