Part A
(a)
Mean  Standard Deviation  
1. Distribution Cost  71.26208333  12.92979437  
2. Sales  456.5  81.53206891  
3.Number of Orders  4393  737.0807873  
The above values have been calculated as: mean=
And the Standard deviation is calculated as S.D. = where is the sample mean and x is sample value while N is the sum of the total terms
4. The Skewness table for Cost:
Cost 

Mean 
71.26208 
Standard Error 
2.639283 
Median 
70.805 
Mode 
#N/A 
Standard Deviation 
12.92979 
Sample Variance 
167.1796 
Kurtosis 
0.82859 
Skewness 
0.28367 
Range 
41.98 
Minimum 
52.46 
Maximum 
94.44 
Sum 
1710.29 
Count 
24 
The Skewness table for Sales:
Sales 

Mean 
456.5 
Standard Error 
16.64266 
Median 
457.5 
Mode 
#N/A 
Standard Deviation 
81.53207 
Sample Variance 
6647.478 
Kurtosis 
0.37714 
Skewness 
0.074334 
Range 
322 
Minimum 
301 
Maximum 
623 
Sum 
10956 
Count 
24 
The Skewness table for Numbers of order received:
Number of orders Received 

Mean 
4393 
Standard Error 
150.456 
Median 
4282.5 
Mode 
#N/A 
Standard Deviation 
737.0808 
Sample Variance 
543288.1 
Kurtosis 
0.45946 
Skewness 
0.052952 
Range 
2814 
Minimum 
2921 
Maximum 
5735 
Sum 
105432 
Count 
24 
As can be seen in the tables the Skewness among the cost is the highest.
(b) The Sample proportion of the all the orders which exceed the 4000 is 0.5 and the Standard deviation for the distribution of the sample proportion is 556.612 as can be found out from the above formula.
(c)
As the number of observations in the sample is less than 30, we use ttest to get the population mean as follows:
Here, is the population mean, is the sample mean, is the t coefficient in the confidence interval with the sample size N=24 and standard Deviation as S.
(i) From above, =71.26 4.3828
Thus, the population mean interval for cost in millions of dollars is 71.26 4.3828
(ii)From above,=456.542.5078
Thus, the population mean interval for Sales in millions of dollars is 456.542.5078.
(iii) From above,=228.2847
Thus, the population mean interval for Number of orders is 228.2847.Please not the sample size is reduced to 12.
(d) The Sample size should be greater than 30 in order, that point estimate is calculated.
(e) Given population mean=65 (In thousand dollars)
Sample mean of the cost=76.21 (In thousand dollars)
Standard deviation of the cost=12.92
Hence, the Z= =0.8882, the corresponding Z score is 0.316
Thus, the claim is correct for significance level 0.05.
(f) Z== 0.97
Which is equivalent to the probability of 0.3389, hence the claim is correct.
(g) The t == 2.56
Whereas, the tvalue should be lower than 2.50.
Hence, the claim is incorrect.
(h)Given population mean=65 (In thousand dollars)
Sample mean of the cost=68.308 (In thousand dollars)
Standard deviation of the cost=10.78
Hence, the Z= =0.306, the corresponding Z score is 0.1406
Thus, the claim is correct for significance level 0.05.
The change in the values is due to the change in the mean and the standard deviation because of the reduced sample size.
Part B
a) For A(c)
(i)
tTest 1sample  
Test Mean 
71.26208 

Confidence Level 
0.95 

N 
24 

Average 
71.26208 
Test Stdev  p 1sample Stdev  
Stdev 
12.92979 
12.92979 
0.922 

SE Mean 
2.639283 

T 
0.000 

TINV 
1.713872 

p – One sided 
0.5 
Accept Null Hypothesis because p > 0.05 (Means are the same)  
p – two sided 
1 
Accept Null Hypothesis because p > 0.05 (Means are the same) 
(ii)
tTest 1sample  
Test Mean 
456.5 

Confidence Level 
0.99 

N 
24 

Average 
456.5 
Test Stdev  p 1sample Stdev  
Stdev 
81.53207 
81.53207 
0.922 

SE Mean 
16.64266 

T 
0.000 

TINV 
2.499867 

p – One sided 
0.5 
Accept Null Hypothesis because p > 0.01 (Means are the same)  
p – two sided 
1 
Accept Null Hypothesis because p > 0.01 (Means are the same) 
iii)
tTest 1sample  
Test Mean 
4576.417 

Confidence Level 
0.9 

N 
12 

Average 
4576.417 
Test Stdev  p 1sample Stdev  
Stdev 
524.1024 
524.1024 
0.887 

SE Mean 
151.2953 

T 
0.000 

TINV 
1.36343 

p – One sided 
0.5 
Accept Null Hypothesis because p > 0.1 (Means are the same)  
p – two sided 
1 
Accept Null Hypothesis because p > 0.1 (Means are the same) 
A(d). The table is similar to A(c)(iii)
A(e).The table is similar to A(c)(i)
A(f)
Test Mean 
3577 

Confidence Level 
0.95 

N 
7 

Average 
3577 
Test Stdev  p 1sample Stdev  
Stdev 
399.6523 
399.6523 
0.846 

SE Mean 
151.0544 

T 
0.000 

TINV 
1.94318 

p – One sided 
0.5 
Accept Null Hypothesis because p > 0.05 (Means are the same)  
p – two sided 
1 
Accept Null Hypothesis because p > 0.05 (Means are the same) 
A(g) The table is similar to A(c)(ii)
A(h).
Test Mean 
68.30833 

Confidence Level 
0.99 

N 
12 

Average 
68.30833 
Test Stdev  p 1sample Stdev  
Stdev 
10.78041 
10.78041 
0.887 

SE Mean 
3.112035 

T 
0.000 

TINV 
2.718079 

p – One sided 
0.5 
Accept Null Hypothesis because p > 0.01 (Means are the same)  
p – two sided 
1 
Accept Null Hypothesis because p > 0.01 (Means are the same) 
PartC
(a)
i)In order to get the model of Cost vs. Sales, we using the least square method, we have the:
Coefficient of Sales=0.13354757
Intercept of Cost= 10.29761784
So, we have: Cost= (0.13354757) sales+10.29761784
ii)In order to get the model of Cost vs. Number of orders Received, we using the least square method, we have the:
Coefficient of Number of orders Received=0.016117564
Intercept of Cost= 0.457625305
So, we have: Cost= (0.016117564) Number of orders Received+0.457625305
(b) The model in part (ii) describes the cost better than (i) because, the coefficient of determination is stronger in the previous one (0.844200772) than the latter case (0.709162344).While the slope of the curves shows the relationship between the two variable the strength of the relationship is shown by the value of Coefficient of determination.
(c)In order to get the model of Cost vs. Sales andNumber of orders Received, we using the least square method, we have the:
Coefficient of Sales=0.047113872
Coefficient of Number of orders Received=0.011946926
Intercept of Cost= 2.728246583
So, we have: Cost= (0.047113872) sales+ (0.011946926) Number of orders Received 2.728246583
(d) For part a (i)
SUMMARY OUTPUT  
Regression Statistics 

Multiple R 
0.842118 

R Square 
0.709162 

Adjusted R Square 
0.695942 

Standard Error 
7.129671 

Observations 
24 

ANOVA  

df 
SS 
MS 
F 
Significance F 

Regression 
1 
2726.822 
2726.822 
53.64357 
2.47E07 

Residual 
22 
1118.309 
50.83221 

Total 
23 
3845.13 


Coefficients 
Standard Error 
t Stat 
Pvalue 
Lower 95% 
Upper 95% 
Lower 95.0% 
Upper 95.0% 
Intercept 
10.29762 
8.449998 
1.218653 
0.235883 
7.22661 
27.82184 
7.22661 
27.82184 
Sales 
0.133548 
0.018234 
7.324177 
2.47E07 
0.095733 
0.171362 
0.095733 
0.171362 
For part a(ii)
SUMMARY OUTPUT  
Regression Statistics 

Multiple R 
0.918804 

R Square 
0.844201 

Adjusted R Square 
0.837119 

Standard Error 
5.218274 

Observations 
24 

ANOVA  

df 
SS 
MS 
F 
Significance F 

Regression 
1 
3246.062 
3246.062 
119.2074 
2.39E10 

Residual 
22 
599.0683 
27.23038 

Total 
23 
3845.13 


Coefficients 
Standard Error 
t Stat 
Pvalue 
Lower 95% 
Upper 95% 
Lower 95.0% 
Upper 95.0% 
Intercept 
0.457625 
6.571883 
0.069634 
0.945114 
13.1716 
14.08688 
13.1716 
14.08688 
Number of orders Received 
0.016118 
0.001476 
10.91821 
2.39E10 
0.013056 
0.019179 
0.013056 
0.019179 
For part c
SUMMARY OUTPUT  
Regression Statistics 

Multiple R 
0.935914 

R Square 
0.875936 

Adjusted R Square 
0.86412 

Standard Error 
4.766166 

Observations 
24 

ANOVA  

df 
SS 
MS 
F 
Significance F 

Regression 
2 
3368.087 
1684.044 
74.1336 
3.04E10 

Residual 
21 
477.043 
22.71633 

Total 
23 
3845.13 


Coefficients 
Standard Error 
t Stat 
Pvalue 
Lower 95% 
Upper 95% 
Lower 95.0% 
Upper 95.0% 
Intercept 
2.72825 
6.15788 
0.44305 
0.66226 
15.5343 
10.07777 
15.5343 
10.07777 
Sales 
0.047114 
0.020328 
2.317693 
0.030644 
0.00484 
0.089388 
0.00484 
0.089388 
Number of orders Received 
0.011947 
0.002249 
5.313123 
2.87E05 
0.007271 
0.016623 
0.007271 
0.016623 
References
1. Rumsey D., Statistics for dummies.
2.Rumsey D., Intermediate Statistics for dummies.
3.SharbBoslough and Andrew Watters, Statistics in a nutshell
4. John Buglear, Stats means Business
5.“Statistics in excel” from http://www.ehow.com
LE94
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