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The production department

 

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, 3 employees were assigned to assemble the subassemblies. They produced 14 during a one-hour period. Then 5 employees assembled them. They produced 23 during a one-hour period. The complete set of paired observations follows.

 

Number of
Assemblers		One-Hour
Production (units)
314
523
29
638
426

 

The dependent variable is production; that is, it is assumed that different levels of production result from a different number of employees.

Click 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?

 

  
    (Click to select) Yes No , as the number of assemblers (Click to select) decreases increases , so does the production.

 

c.Compute the correlation coefficient. (Negative amounts should be indicated by a minus sign. Round sx, sy and r to 3 decimal places.)

 

XY( )2( )2( )( )
314 -8 64 
5231 1 1
29 -13 169 
6382 4 32
426 40 0
       

 

= = sx= 

 

sy=  r= 
 

2.

The following sample observations were randomly selected. (Round your answers to 2 decimal places.)

 

X:453610
Y:9.810.6713.419.6

 

a. The regression equation is   = + X
  
b. When X is 7 this gives =
      
       

 

The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year.

 

CarAge (years)Selling Price ($000)CarAge (years)Selling Price ($000)
198.1787.6
276.08118.0
3113.69108.0
4124.010126.0
585.01168.6
6710.01268.0

 Click here for the Excel Data File

a.If we want to estimate selling price on the basis of the age of the car, which variable is the dependent variable and which is the independent variable?
  
    (Click to select) Car Selling price Age  is the independent variable and (Click to select) selling price age car  is the dependent variable.

 

4.

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

 

XY( )2( )2( )( )
9.08.1 1.1920.0071.4200.099
7.06.0 -0.9083.6740.8251.741
11.03.62.083 4.34010.945-6.892
12.04.03.083 9.5078.458-8.967
8.05.0-0.917-1.908 3.6421.749
7.010.0-1.9173.092 9.558-5.926
8.07.6-0.9170.6920.840 -0.634
11.08.02.0831.0924.340 2.274
10.08.01.0831.0921.1741.192 
12.06.03.083-0.9089.5070.825 
6.08.6-2.9171.6928.5072.862-4.934
6.08.0-2.9171.0928.5071.192-3.184
107.00082.900     

 

==sx=sy=

 

r=

 

b-2.Determine the coefficient of determination. (Round your answer to 3 decimal places.)
  
 

 

c.Interpret the correlation coefficient. Does it surprise you that the correlation coefficient is negative? (Round your answer to nearest whole number.)
  
    (Click to select) No Moderate Strong correlation between age of car and selling price. So,  % of the variation in the selling price is explained by the variation in the age of the car.
  

 

5.

Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 20 stations last Tuesday, the correlation was .78.

 

At the .01 significance level, is the correlation in the population greater than zero? (Round your answer to 3 decimal places.)

 

  The test statistic is .

 

Decision: (Click to select) Reject Do not reject H0: ρ ≤ 0

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