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 t-test 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 t-value 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)

 t-Test 1-sample Test Mean 71.26208 Confidence Level 0.95 N 24 Average 71.26208 Test Stdev p 1-sample 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)

 t-Test 1-sample Test Mean 456.5 Confidence Level 0.99 N 24 Average 456.5 Test Stdev p 1-sample 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)

 t-Test 1-sample Test Mean 4576.417 Confidence Level 0.9 N 12 Average 4576.417 Test Stdev p 1-sample 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 1-sample Stdev Stdev 399.652 399.6523 0.846 SE Mean 151.054 T 0 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 68.3083 Confidence Level 0.99 N 12 Average 68.3083 Test Stdev p 1-sample Stdev Stdev 10.7804 10.78041 0.887 SE Mean 3.11204 T 0 TINV 2.71808 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)

Part-C

(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 2.47E-07 Residual 22 1118.309 50.83221 Total 23 3845.13 Coefficients Standard Error t Stat P-value 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 2.47E-07 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 2.39E-10 Residual 22 599.0683 27.23038 Total 23 3845.13 Coefficients Standard Error t Stat P-value 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 2.39E-10 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 3.04E-10 Residual 21 477.043 22.71633 Total 23 3845.13 Coefficients Standard Error t Stat P-value 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 2.87E-05 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

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