Part A

(a)

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:

The Skewness table for Sales:

The Skewness table for Numbers of order received:

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)

(ii)

iii)

A(d). The table is similar to A(c)(iii)

A(e).The table is similar to A(c)(i)

A(f)

A(g) The table is similar to A(c)(ii)

A(h).

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)

For part a(ii)

For part c

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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