Stat quistions

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, 2 employees were assigned to assemble the subassemblies. They produced 15 during a one-hour period. Then 4 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

7

5

28

3

20

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?

  (Click to select)NoYes , as the number of assemblers (Click to select)increasesdecreases, so does the production.

c.

Compute the correlation coefficient. (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  

-4  

16  

4  

25  

1  

1  

6  

1  

7  

-12  

144  

5  

28  

2  

4  

18  

3  

20  

1  

0  

0  

=

=

s_x

=

s_y

=

r

=

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

X:

4

5

3

6

10

Y:

8.8

12.6

7

14.4

18.6

a.

 The regression equation is   = + X

b.

 When X is 6 this gives  =  

Bi-lo Appliance Super-Store has outlets in several large metropolitan areas in New England. The general sales manager aired a commercial for a digital camera on selected local TV stations prior to a sale starting on Saturday and ending Sunday. She obtained the information for Saturday–Sunday digital camera sales at the various outlets and paired it with the number of times the advertisement was shown on the local TV stations. The purpose is to find whether there is any relationship between the number of times the advertisement was aired and digital camera sales. The pairings are:

  Location of

Number of

Saturday–Sunday Sales

  TV Station

Airings

($ thousands)

  Providence

4

15

  Springfield

2

8

  New Haven

5

21

  Boston

6

24

  Hartford

3

17

Click here for the Excel Data File

a.

What is the dependent variable?

(Click to select)Number of advertisementsSales is the dependent variable.

c.

Determine the correlation coefficient. (Round your answer to 2 decimal places.)

  Coefficient of correlation

d.

Interpret these statistical measures.

  The statistical measures obtained here indicate (Click to select)a strong positivea strong negative correlation between the variables.

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.

Car

Age (years)

Selling Price ($000)

Car

Age (years)

Selling Price ($000)

1

9

8.1

7

8

7.6

2

7

6.0

8

11

8.0

3

11

3.6

9

10

8.0

4

12

4.0

10

12

6.0

5

8

5.0

11

6

8.6

6

7

10.0

12

6

8.0

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)AgeCarSelling price is the independent variable and (Click to select)selling priceagecar is the dependent variable.

b-1.

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

X

Y

( )²

( )²

( )( )

9.0  

8.1  

1.192  

0.007  

1.420  

0.099  

7.0  

6.0  

-0.908  

3.674  

0.825  

1.741  

11.0  

3.6  

2.083  

4.340  

10.945  

-6.892  

12.0  

4.0  

3.083  

9.507  

8.458  

-8.967  

8.0  

5.0  

-0.917  

-1.908  

3.642  

1.749  

7.0  

10.0  

-1.917  

3.092  

9.558  

-5.926  

8.0  

7.6  

-0.917  

0.692  

0.840  

-0.634  

11.0  

8.0  

2.083  

1.092  

4.340  

2.274  

10.0  

8.0  

1.083  

1.092  

1.174  

1.192  

12.0  

6.0  

3.083  

-0.908  

9.507  

0.825  

6.0  

8.6  

-2.917  

1.692  

8.507  

2.862  

-4.934  

6.0  

8.0  

-2.917  

1.092  

8.507  

1.192  

-3.184  

107.000  

82.900  

=

=

s_x

=

s_y

=

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)StrongNoModerate 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.

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)RejectDo not reject H₀: ρ ≤ 0