Costumer satisfaction is always the top priority of any service and product oriented business establishments. Assuring that the costumer gets the maximum satisfaction he needs and seeks to find is the top concern of any operating personnel of different business establishment. One way of assuring the customer satisfaction is maintain the high quality standards of the products sold. Thus, it is the top duty of the quality manager to maintain or even elevate the quality standard that the company is maintaining at present. Thus, this paper is to give the company an eagle’s eye view of the quality of the product it is serving to the public at present.

## Project No. 1

The process was simple. Three bags of M&Ms® were bought from 3 different stores and each color of candies in each bag were counted and tabulated. Table 1.1 shows the result of the sampling done:

 Blue Orange Green Yellow Red Brown Num. of Candies in Bag bag 1 13 17 2 8 9 8 57 bag 2 3 13 13 9 8 11 57 bag 3 14 9 14 8 3 9 57

Table 1.1 Number of colored chocolates in a bag of  PLAIN M&M®

As can be glanced from the table, each bag contains equal number of candies but the distribution of these candies according to color is not the same per bag. In bag 1, blue and orange dominates while orange and green dominate in the bag 2 and blue and green dominate the bag 3. This initially shows that there were no constant color that dominates the three bags nor there were no color that constantly has lowest number.

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## Project Part 2

The data generated in the part 1 were used to get the proportions of each color in the whole sample. Note that Microsoft Excel was used in calculating the proportions of different colors of candies. Further, the sample mean was also computed and the standard deviation of sample was computed using the apllications in Microsoft Excel.

The results shows that in a bag of M&Ms®, candies were distributed as follows; 24.46% were blue, 20.93% were orange, 16.74% were green, 13.52% were yellow, 11.17% were red, and 13.19% were brown. Moreover, it was calculated that the average number of candies in  a abg of M&Ms® is 55. 61 candies and a standard deviation is 1.9784 which means that if we assume that the candies in bags of M&Ms®  are in normal distribution 68% of the bag of M&Ms® produced contain candies between 53.6316 to 57.5884 candies.

It is also evident in the results in project part 2 (please refer to the attached MS Excel file) that 81 bags are sampled containing a total of 4,505. If we assume the above proportions as true, 1101.923 out 4505 are blue, 942.8965 were orange,  754.137 are green, 609.076 are yellow, 503.2085 are red and 594.2095 are brown.

Project Part 3:

Data gathered in sampling were treated statistically and the confidence intervals of different colors were computed. The table 1.2 below shows the summary of the results.

 95% Confidence interval for From To Blue 0.2320 0.2572 Orange 0.1974 0.2212 Green 0.1565 0.1783 Yellow 0.1252 0.1452 Red 0.1025 0.1209 Brown 0.1220 0.1418 Mean number of candies per bag 55.1864 56.0481

## Table 1.2 95% Confidence interval of different color of candies

The formula     from Introduction to statistics by Ronald E. Walpole is used in the computation of the 95% confidence interval of different colors of candies. Confidence interval serves as our upper and lower limits of expectation. And since we are using 95% confidence interval then we can say that we are 95% confident that in a bag of M&M® candies, the blue candy is about 23.20% to 25.72%. Thus the result shows us the possible distribution in percent of candies according to color in any bag of M&M®. As for the mean number of candies per bag, we can say that the result suggests that the company is 95% confident that a bag of M&M® candies contain 55 – 56 candies.

## Project Part 4

The Mastersfoods USA, claimed that in a bag of M&Ms® milk chocolate candies, 24% are blue candies, 20% are orange, 165 are green, 14% are yellow, 13% are red and 13% are brown. Testing their claim at 0.05 level of significance, the following results can be achieved. Note that the formula    in testing the proportions of different colors.

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v  The claim of the company that there is 24% of blue candies in a bag of M&Ms® is failed to rejected. This means that there is no reason to doubt the company’s claim.

v  The claim of the company that there is 20% of orange candies in a bag of M&Ms® is failed to be rejected. This supports the claim of the company.

v  The claim of the company that there is 16% of green candies in a bag of M&Ms® is failed to be rejected. This means that there is no reason to doubt the company’s claim.

v  The claim of the company that there are 14% of orange candies in a bag of M&Ms® is failed to be rejected. This supports the claim of the company.

v  The claim of the company that there are 13% of red candies in a bag of M&Ms® is rejected. This means that the claim of the company is not true. Either there were more red candies than their claim or there were less. Whichever is true, this is a clear manifestation that there is a lapse in packaging of the product. The investigation must first focus on the bagging process. It could be that the working condition of the plant is not good for the workers that made them tired in all day work.

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v  The claim of the company that there are 13% of brown candies in a bag of M&Ms® is failed to be rejected. This supports the claim of the company.

## Project Part 5

The data generated from the sample were tested using    . It was found out that the claim of the company that the proportion of the red candies and brown candies are equal is being rejected. Thus, there is no evidence that will support to the company’s claim. It can be conclude that in any bag of M&Ms®, there will be more red than brown or the other way around.

## Conclusion

Based on the data presented and on the statistical results from tests being conducted, the following conclusions can be drawn.

That there is enough evidence of the claim of the Mastersfoods USA that in every bag of M&Ms®, there are 24% blue candies, 20% orange candes, 16%green, 14% yellow candies and 13% brown candies.

That there is no enough evidence of the claim of the Mastersfoods USA that in every bag of M&Ms®, there are 13% red candies.

That the Mastersfoods USA should consider investigating the bagging process in the company to check and recheck the effectiveness of the employees.

That the Mastersfoods USA should consider conducting a similar research with more sample included and more precision is imposed.

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