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

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

ECF6102 Quantitative Skills for Business Proof Reading Services