Two Population Means QNT/351 Version 5 University of Phoenix 5

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Two Population Means

A tomato farmer with a very large farm of approximately 2200 acres had heard about a new type of rather expensive fertilizer which would supposedly significantly increase his production. The frugal farmer wanted to test the new fertilizer before committing the large investment required to fertilize a farm of his size. He therefore selected 15 parcels of land on his property and divided them each into two portions.  He bought just enough of the new fertilizer to spread over one half of each parcel and then spread the old fertilizer over the other half of each parcel. His yields in pounds per tomato plant were as follows:

Parcel

New Fertilizer

Old Fertilizer

1

14.2

14.0

2

14.1

13.9

3

14.5

14.4

4

15.0

14.8

5

13.9

13.6

6

14.5

14.1

7

14.7

14.0

8

13.7

13.7

9

14.0

13.3

10

13.8

13.7

11

14.2

14.1

12

15.4

14.9

13

13.2

12.8

14

13.8

13.8

15

14.3

14.0

The farmer had taken statistics many years ago when in college and consequently made a couple of mistakes when testing to find if the new fertilizer was more effective:  (1) He tested the data as two independent samples, and (2) He performed a two-tailed test. He decided that he was unable to conclude that there was a difference between the two fertilizers. 

What if you were the fertilizer sales representative and your job was to prove the superiority of the new product to the farmer?

(1)    You should start by running the same test he did in which he came to the decision that he could not conclude a difference. 

(2)    Perform the test as it should have been done and find if you come to a different conclusion.

(3)    Explain why the results were different and why your test was a stronger and more reliable test. 

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 8 during a one-hour period. Then 5 employees assembled them. They produced 13 during a one-hour period. The complete set of paired observations follows.

Number of

Assemblers

One-Hour

Production (units)

3

8

5

13

2

5

6

23

4

16

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)YesNo , as the number of assemblers (Click to select)decreasesincreases, 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.)

X

Y

( )²

( )²

( )( )

3  

8  

-5  

25  

5  

13  

1  

1  

0  

2  

5  

-8  

64  

6  

23  

2  

4  

20  

4  

16  

3  

0  

0  

=

=

sx

=

sy

=

r

=

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

X:

4

5

3

6

10

Y:

8.8

13.6

8

15.4

19.6

a.

 The regression equation is   = + X

b.

 When X is 5.5 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)SalesNumber of advertisementsis 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 negativea strong positive

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

 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)CarAgeSelling 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  

=

=

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)NoModerateStrong 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 rejectH0: ρ ≤ 0