MATHEMATICS

1)       The following sample observations were randomly selected.

 

   X :    4        5         3         6      10
Y:    4        6          5         7      7

 

PictureClick here for the Excel Data File

 

(1) Fill in the blanks below: (Round your answers to 2 decimal places.)

 

   
  Picture 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 one-hour period. Then four employees assembled them. They produced 25 during a one-hour period. The complete set of paired observations follows.

 

Number of
Assemblers
One-Hour
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.

 

PictureClick here for the Excel Data File

 

(b) A scatter diagram is provided below. Based on it, does there appear to be any relationship between the number of assemblers and production?

 

   Picture
    , 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 sx, sy and r  to 3 decimal places.)

 

X Y Picture Picture (Picture )2 (Picture )2 (Picture )(Picture )
2 15  is the independent variable and is the dependent variable.

 

(b-1) Determine the coefficient of correlation. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

 

X Y Picture Picture (Picture )2 (Picture )2 (Picture )(Picture )
9.0 8.1 correlation between age of car and selling price. So, Ho. Weconclude that the correlation in the population is
greater than zero.

 

7)       The following hypotheses are given.

 

  formula198.mml
  formula199.mml

 

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 H0 if t < −1.771 t =   Ho.

 

 

 

 

 

8)       The following sample observations were randomly selected.

 

PictureClick here for the Excel Data File

 

 
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 Picture Picture (Picture)2 (Picture)2 (Picture )(Picture )
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]

 

  Picture = [removed]     Picture = [removed]     sx = [removed]

 

sy = [removed]   r = [removed]

 

b = [removed]   a = [removed]

 

  Y’ = [removed]+ [removed]X

 

(b) Determine the value of formula264.mmlwhen X is 7. (Round your answer to 3 decimal places.)
   
  [removed]

 

9)       Bradford Electric Illuminating Company is studying the relationship between kilowatt-hours (thousands) used and the number of rooms in a private single-family residence. A random sample of 10 homes yielded the following.

 

Number of Rooms Kilowatt-Hours (thousands) Number of Rooms Kilowatt-Hours (thousands)
12   9   8   6  
9   7   10   8  
14   10   10   10  
6   5   5   4  
10   8   7   7  

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