ECF6102 Quantitative Skills for Business Proof Reading Services

ECF6102 Quantitative Skills for Business Oz Assignment

ECF6102 Quantitative Skills for Business Proof Reading Services

Part A

Question a

Mean and Standard deviation

Cost

Sales

Orders

52.95

386

4015

71.66

446

3806

85.58

512

5309

63.69

401

4262

72.81

457

4296

68.44

458

4097

52.46

301

3213

70.77

484

4809

82.03

517

5237

74.39

503

4732

70.84

535

4413

54.08

353

2921

62.98

372

3977

72.3

328

4428

58.99

408

3964

79.38

491

4582

94.44

527

5582

59.74

444

3450

90.5

623

5079

93.24

596

5735

69.33

463

4269

53.71

389

3708

89.18

547

5387

66.8

415

4161

 

Cost

Sales

Orders

Mean

71.26

456.50

4,393.00

Standard Deviation

12.93

81.53

737.08

Question b

Standard deviation of all orders above 4,000

Sample proportion

Orders above 4000

4015

5309

4262

4296

4097

4809

5237

4732

4413

4428

4582

5582

5079

5735

4269

5387

4161

Mean

4,729.00

Standard deviation

556.61

Question c

Confidence intervals

95% for distribution cost

http://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_confidence_intervals/lessonimages/equation_image106.gif

Since the total value is less than 30, t distribution is used to measure the confidence interval

i)

Cost

Mean

71.26

Standard Deviation

12.93

Sqrt n

4.90

t

2.07

CI

 

Upper limit

76.72

Lower limit

65.80

99% confidence interva on sales

ii)

Sales

Mean

456.50

Standard Deviation

81.53

Sqrt n

4.90

t

2.81

CI

 

Upper limit

503.22

Lower limit

409.78

90% confidence interval on orders exceed 4000

iii)

Orders

Mean

4,729.00

Standard Deviation

556.61

Sqrt n

4.90

t

1.75

CI

 

Upper limit

4,927.36

Lower limit

4,530.64

Question d

Point estimate

Mean

4,729.00

Standard Deviation

556.61

Normal dist

4,015.67

N = (z/M)^2 x p (1-p)

Z

1.96

population

0.1

  

Margin of error

222.69

Sample Size

7.02

Question e

Null hypothesis: The mean is equal to 65

Alternate hypothesis: The mean is not equal to 65

x

71.26

Standard Deviation

12.93

Mu

65

n

24

t dist

2.37

t table value

2.07

Since t distribution is greater than t table value the null hypothesis is rejected and alternate hypithesis is accepted

Question f

Null hypothesis: 30% orders received are less than 4000

Alternate hypothesis: 30% orders received are not less than 4000

Mean

4,393.00

SD

737.08

Mu

4000

n

24

t dist

2.61

p value

0.007828

The result is significant at p < .05.

Question g

Cost

52.95

71.66

85.58

63.69

72.81

68.44

52.46

70.77

82.03

74.39

70.84

54.08

Null hypothesis: The mean is equal to 65

Alternate hypothesis: The mean is not equal to 65

Mean

68.31

SD

10.78

Mu

65

n

12

t dist

1.06

t table value

3.11

Since t distribution is less than t table value the null hypothesis is accepted

Part B

Question a

Question b

Question c

Question d

Question e

Question f

Part C

Question a

Cost and Sales

 

 

 

 

 

 

 

 

SUMMARY OUTPUT

       

 

 

       

 

Regression Statistics

      

 

Multiple R

0.842117773

      

 

R Square

0.709162344

      

 

Adjusted R Square

0.69594245

      

 

Standard Error

7.129671393

      

 

Observations

24

      

 

 

       

 

ANOVA

       

 

 

df

SS

MS

F

Significance F

  

 

Regression

1

2726.821684

2726.821684

53.64357481

2.47416E-07

  

 

Residual

22

1118.308712

50.83221418

    

 

Total

23

3845.130396

 

 

 

  

 

 

       

 

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

10.29761784

8.449998094

1.218653274

0.235882952

-7.226605545

27.82184123

-7.226605545

27.82184123

Sales

0.13354757

0.018233798

7.324177415

2.47416E-07

0.095732988

0.171362151

0.095732988

0.171362151

Cost and Orders

 

 

 

 

 

 

 

 

SUMMARY OUTPUT

       

 

 

       

 

Regression Statistics

      

 

Multiple R

0.91880399

      

 

R Square

0.844200772

      

 

Adjusted R Square

0.837118989

      

 

Standard Error

5.218273602

      

 

Observations

24

      

 

 

       

 

ANOVA

       

 

 

df

SS

MS

F

Significance F

  

 

Regression

1

3246.062049

3246.062049

119.2073751

2.38511E-10

  

 

Residual

22

599.0683465

27.23037939

    

 

Total

23

3845.130396

 

 

 

  

 

 

       

 

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

0.457625305

6.571882688

0.069633821

0.945114194

-13.17162514

14.08687576

-13.17162514

14.08687576

Orders

0.016117564

0.001476209

10.918213

2.38511E-10

0.013056094

0.019179034

0.013056094

0.019179034

Based on the above outputs it is identified that the value of R square betwee cost and sales is 0.7091 or 70.91% whereas the value is 0.8442 or 84.42% for cost and orders. The value of R square intends to specify the goodness of the fit of the model, the maximum value of R square is 1 or 100%, so higher the value of R square better is the goodness of fit to the model. So it can be stated that cost and orders shows a better association in the model

Question c

Multiple regression

Cost - Sales and Orders

 

 

 

 

 

 

 

 

SUMMARY OUTPUT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Regression Statistics

 

 

 

 

 

 

 

 

Multiple R

0.93591442

 

 

 

 

 

 

 

R Square

0.875935802

 

 

 

 

 

 

 

Adjusted R Square

0.864120164

 

 

 

 

 

 

 

Standard Error

4.766165573

 

 

 

 

 

 

 

Observations

24

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ANOVA

 

 

 

 

 

 

 

 

 

df

SS

MS

F

Significance F

 

 

 

Regression

2

3368.087376

1684.043688

74.1336022

3.0429E-10

 

 

 

Residual

21

477.0430196

22.71633427

 

 

 

 

 

Total

23

3845.130396

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

-2.728246583

6.157879754

-0.443049668

0.662260247

-15.53425853

10.07776536

-15.53425853

10.07776536

Sales

0.047113872

0.02032792

2.317692762

0.030643769

0.004839649

0.089388095

0.004839649

0.089388095

Orders

0.011946926

0.002248569

5.313123092

2.87239E-05

0.00727077

0.016623082

0.00727077

0.016623082

By using multiple regression where in the sales and orders are considered as independent variables ad the dependent variable is cost. The model states that the R square is 0.8759 or 87.59% which is a better fit when compared with individual models which was specified in question a. Also the significance value is 0.00 which shows that there is a significant relationship between the independent variables and the dependent variable.

Based on the regression coefficients the regression equation can be stated as

Y (Cost) = Constant + X1 (Sales) + X2 (Orders)

Y (Cost) = -2.73 + 0.047 (Sales) + 0.0119 (Orders)

Based on the above it is noted that orders possess a significant influence on the cost when compared with sales

Part D

Question a

F test

Null hypothesis: There is no significant variance of the waiting time between the two branches

Alternate hypothesis: There is a significant variance of the waiting time between the two branches

 

CBD

Suburban

Mean

4.286666667

6.873571429

Variance

2.682995238

3.73004011

Observations

15

14

df

14

13

F

0.719293938

 

P(F<=f) one-tail

0.274097371

 

F Critical one-tail

0.398841227

 

Based on the above table it is identified that the p value is 0.274 which is more than the sig value of 0.05 (5%) so the null hypothesis is accepted. Hence it is stated that There is no significant variance of the waiting time between the two branches

Question b

Based on the overall analysis it is identified that the t-Test: Paired Two Sample for Means can be used

Question c

Null hypothesis: There is no difference in the mean waiting time between the two branches

Alternatehypothesis: There is a difference in the mean waiting time between the two branches

 

CBD

Suburban

Mean

4.286666667

7.114666667

Variance

2.682995238

4.335512381

Observations

15

15

Pearson Correlation

0.176721009

 

Hypothesized Mean Difference

0

 

df

14

 

t Stat

-4.542789694

 

P(T<=t) one-tail

0.000229993

 

t Critical one-tail

1.761310136

 

P(T<=t) two-tail

0.000459985

 

t Critical two-tail

2.144786688

 

Based on the above table it is identified that the p-value is 0.00 which is less than the sig value of 0.05 (5%) so the null hypothesis is rejected and alternate hypothesis is accepted. Hence, There is a difference in the mean waiting time between the two branches.

References

1. Boslaugh, Sarah (2012). Statistics in a Nutshell. Cengage Publishing

2. Freedman, David (2010). Statistics. 4th Edition. Cengage Publishing

3. Sincich, T. Terry (2012). Statistics. 12th Edition.

4. Triola (2014). Essentials of Statistics. 5th Edition. McGraw Hill

5. Witte, S. Robert. (2010). Statistics. 5th Edition. McGraw Hill