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- July 4, 2020

# Chi-Square Analysis Paper

CHI-SQUARE ANALYSIS 4

Chi-SquareAnalysis Paper

Chi-SquareAnalysis

Whenbags of M&M candies are produced by the Mars Company, theincorporated machines are expected to deliver a certain proportion ofeach color of M&M (Madison,2016).Although the company claims that each batch of candies is blended inthe proportions as shown in the website, the possibility of having anunusual color distribution is expected. To determine whether thecompany’s claim is true, a chi-square analysis can be carried. According to Weis (2016), the Chi-square goodness of fit test helpsin determining the validity of the hypothesized distribution.

Hypothesis

Thenull hypothesis (*H*_{0}):The Company’s color proportion for the M&M candies as stated onthe website is correct.

Thealternative hypothesis (*H*_{1}):Thecolor distribution as stated by the company is not correct.

Assumptions

Thefirst assumption made in carrying out the test is that a sample bagof all the M&Ms produced was obtained. The second one is that thesample was large enough to carry out the test. The sampling was donewithout replacement, therefore there is a possibility that thesample selected is 1/10 of the total.

Significancelevel (α)

Basedon several studies, the significance level can be selected as 0.05.According to Brown (2015), scientists suggest that if the probabilityof achieving the expected distribution by chance is greater than 5%,then the null hypothesis holds.

Discussionand Conclusion

Thep-value obtained is 0.0749, which according to Weis (2016), it refersto the relative frequency or probability for the value in the nullhypothesis. Since it is larger than the significance level (>0.05),it can be concluded that there is no significant difference in theactual ratios of the M&M colors as claimed by the Mars Company.This also implies that any difference that might be seen will havejust happened by chance. The sample size has a significant impact onthe results. Selecting a larger sample would give more accurateresults as it will present a greater proportion of the population. Ina chi-square goodness-of-fit test, the expected frequency (E) isgiven by

Wheren is the sample size and p is the significance level (Weis, 2016).From the formula, it can be noted that a larger sample size willproduce a higher expected frequency and hence more accurate results.

References

Brown,S. (2015, January 21). Stats without Tears12. Tests on Counted Data.Retrieved from http://brownmath.com/swt/chap12.htm

Madison,J., (2016). M&M’s Color Distribution Analysis. Retrieved fromhttp://joshmadison.com/mms-color-distribution-analysis/

Weiss,N. A. (2016). Introductory Statistics (10th ed.). New York, NY:Pearson Education.