Problem Set, statistic homework help

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LBYB2013

Mathematics

Description

1. 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 13 during a one-hour period. Then 4 employees assembled them. They produced 22 during a one-hour period. The complete set of paired observations follows.

Number of One-Hour Assemblers Production (units)

2 13

4 22

1 9

5 36

3 25

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?

(yes or no), as the number of assemblers (decreases or 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.)

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

  • The regression equation is
  • When X is 7 this gives

3. 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

a. What is the dependent variable?

(Number of Advertisements or Sales) is the dependent variable.

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

Coefficient of correlation (?????)

c. Interpret these statistical measures.The statistical measures obtained here indicate (a strong positive or a strong negative) correlation between the variables.

4. 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?

(Selling price, Car, or Age) is the independent variable and (selling price, age, or car) 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.) See Attachment.

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.)

(Strong, No, or Moderate) 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: (Reject or Do not reject) Ho : p ≤ 0

😊"SEE ATTACHMENT FOR CHARTS AND A BETTER UNDERSTANDING OF EACH QUESTION"😊



Unformatted Attachment Preview

1. 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 13 during a one-hour period. Then 4 employees assembled them. They produced 22 during a one-hour period. The complete set of paired observations follows. Number of Assemblers 2 4 1 5 3 One-Hour Production (units) 13 22 9 36 25 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? (yes or no), as the number of assemblers (decreases or 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.) Worksheet Objective: Calculate a correlation coefficient to test and interpret the relationship between two variables. 2. The following sample observations were randomly selected. (Round your answers to 2 decimal places.) X: Y: a. b. 4 9.8 5 12.6 3 8 6 15.4 10 19.6 The regression equation is When X is 7 this gives = + X = 3. 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 TV Station Providence Springfield New Haven Boston Hartford Number of Airings 4 2 5 6 3 Saturday–Sunday Sales ($ thousands) 15 8 21 24 17 a. What is the dependent variable? (Number of Advertisements or Sales) 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 (a strong positive or a strong negative) correlation between the variables. Worksheet Objective: Calculate a correlation Co-efficient to test and interpret the relationship between two variables. 4. 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 7 11 12 8 7 2 3 4 5 6 6.0 3.6 4.0 5.0 10.0 8 9 10 11 12 11 10 12 6 6 8.0 8.0 6.0 8.6 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? (Selling price, Car, or Age) is the independent variable and (selling price, age, or car) 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 9.0 8.1 1.192 )2 0.007 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 6.0 107.000 8.6 8.0 82.900 -2.917 -2.917 1.692 1.092 8.507 8.507 2.862 1.192 = ( = sx = 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.) (Strong, No, or Moderate) 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. ( )2 1.420 ( )( ) 0.099 -4.934 -3.184 sy = Worksheet Objective: Calculate a correlation coefficient to test and interpret the relationship between two variables. 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: (Reject or Do not reject) Ho : p ≤ 0 Worksheet Objective: Calculate a correlation coefficient to test and interpret the relationship between two variables.
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Explanation & Answer

HiPlease find the answer in docs file with explanation in excel sheet.Thank you.

Number of

One-Hour
x

Sum

x-xbar

y
2

13

4

22

1

9

5

36

3

25

15

105

XBAR=3
Ybar =21
sx
sy

1,581
10,607

r

0,939

y-ybar
-1
1
-2
2
0
0

(x-xbar)^2
-8
1
-12
15
4
0

(y-ybar)^2
1
1
4
4
0
10

64
1
144
225
16
450

(x-xbar)(y-ybar)
8
1
24
30
0
63

X

Y
4
5
3
6
10

SUMMARY OUTPUT
9,8
12,6
8
15,4
19,6

Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations

0,9725
0,9457
0,9276
1,2377
5

ANOVA
df
Regression
Residual
Total

Intercept
X

SS
1 80,09211
3 4,59589
4
84,688

Coefficients
Standard Error
3,81 1,397025
1,66 0,229051

Equation
y=3.81+1.66x
Value ,x=7

MS
F
Significance F
80,09211 52,28069 0,005455
1,531963

t Stat
P-value Lower 95% Upper 95%Lower 95.0%
Upper 95.0%
2,723988 0,072306 -0,64048 8,251437 -0,64048 8,251437
7,230539 0,005455 0,927221 2,385108 0,927221 2,385108

15,40

Location

Total
Airlings

Sales

Providence

4

15

Springfield

2

8

New Haven

5

21

Boston

6

24

Hartford

3

17

Correlation Coefficient

0,93

Age,X

Selling Price,Y
9
7
11
12
8
7
8
11
10
12
6
6
107

Sum

x-xbar
8,1
6
3,6
4
5
10
7,6
8
8
6
8,6
8
82,9

Xbar
Y-bar

8,917
6,908

sx
sy

2,234
1,968

r
Rsquare

-0,544
0,30

y-ybar
0,083
-1,917
2,083
3,083
-0,917
-1,917
-0,917
2,083
1,083
3,083
-2,917
-2,917
0,000

(X-Xbar)^2
1,192
-0,908
-3,308
-2,908
-1,908
3,092
0,692
1,092
1,092
-0,908
1,692
1,092
0,000

0,007
3,674
4...


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