# MATHEMATICS

 1)       The following sample observations were randomly selected.

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

 (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 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.

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

 X Y ( )2 ( )2 ( )( ) 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 ( )2 ( )2 ( )( ) 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.

 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.

 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] sx = [removed]

 sy = [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 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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