The Organizational and National Statistics
Introduction
The Coca – Cola Company is the distributor, manufacturer, and marketer for the non-alcoholic syrups and the beverage concentrates to the whole world. The company licenses and owns greater than 450 brands which includes lights and diet beverages, enhanced waters, juices, and juice drinks, coffees, and sports and energy drinks (, 2008).
The table shows the quarterly revenue of the company for the year 2004.
The Coca-Cola Company for Quarters for the year 2004
In Millions
1Q04
2Q04
3Q04
4Q04
North America
,426
,702
,699
,517
Latin America
483
485
522
552
Europe, Eurasia and Middle East
1,303
1,824
1,820
1,609
Africa
175
181
197
274
Asia
1,086
1,444
1,382
1,140
Corporate
29
59
51
84
Total
,502
,695
,671
,176
Source: The Coca Cola Company Annual Report
The data below shows the graph of its revenues:
The mean for the revenues of the data is 0 which signifies that the revenues of the company for all over the world has the average of 0 Million for the quarter 1 but the quarter 2 had the highest mean for having the revenue of 9 million. The median of 5 million for the second quarter means the amount for the half of the revenues of the company.
The predicted value for next quarter can be predicted using the regression formula of y = mx +b where m is the slope.
Regression
In Quarters
North America
Latin America
Europe, Eurasio
and Middle East
Africa
Asia
Corporate
1
,426
483
1,303
175
1,086
29
2
,702
485
1,824
181
1,444
59
3
,699
522
1,820
197
1,382
51
4
,517
552
1,609
274
1,140
84
5
53.5
1.5
,867.5
5
,288
This implies that 53.5 million is expected for next quarter in North America, 1.5 million in the Latin America, ,867.5 million in Middles and to other regions, 5 to Africa, and ,288 million in Asia which means that the Middle East, Eurasia and Europe still has the highest expected revenue for the next quarter.
The Coca Cola Company made the machine which can manufactures the sodas and has the mean expiration lifetime of only 5,000 hours, in line with this; it has also the recorded standard deviation of 160 hours. Nevertheless, the company is not satisfied to the performance of the said machine and decided to consider buying the new machine which can has the ability to make longer expiration life to the soda as it can last longer than the used old machinery. The company made the sample of 200 sodas produced from the new machine which has the lifetime mean of 5020 hours. The problem therefore that Coca-Cola is facing is if the new machine can produce the longer expiration life to the soda so that they can buy the new machine.
In this manner, the hypothesis testing can be use in order for the company to decide whether to accept the new machine or the sample is compatible to the true mean of being larger.
1. Determine the hypothesis
Ho = μ > 5000
H1 = μ > 5000
2. This means that the lifetime experience is greater than 5000 hours and it is presumably a one tailed test or to make more specific it is the right tailed-test. In order to make more accurate we have to choose the 99% confidence interval and it requires the number of 2.33.
3. The standard error can also be calculated using the formula:
Standard error = ό / √ n
= 160 / √ 200
= 160 / 14.14
= 11.31
4. Calculation for the Critical Region
The calculation for the critical region which has the mean from the sample has no upper limit. On the other hand, the lower limit is equal to x bar - 2.33 S.E. therefore = 5020 – 2.33 X 11.31 which yields to 4993.65.
This critical region simply means that 99% certainty in the mean lifetime for the sodas can be produce by the new machine are lying in the said region. This implies that the 1% for the chance simply means will be less than the 4993.65 if the mean being established will lie on the region and it is compatible to the mean for the sodas lifetime and to the machine.
5. Comparison of the established value and the true mean to the critical region
The 5000 is not smaller to the 4993.65 and the established mean is within the critical region. This implies that it is acceptable for the Ho and needs to reject the H1. The mean lifetime for the sodas therefore is higher than 5,000 which is as the 1% of the significance level and implies that the machine cannot produce the longer lasting lifetime before expiration. Thus, the advice for the company is to stick into the machine or just properly used the old machine.
The relationship of the revenues in the 1st quarter and the 4th quarter can be determined by using the formula of correlation or get the value of r
The 1st and the 4th quarters have the 0.991255 value of r which means that the two variables are strongly correlated or they are related significantly.
Credit:ivythesis.typepad.com
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