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M & M Project

M & M Project Report 1 M & M Project Report Jaquetta McGee Strayer University M & M Project Report Abstract The purpose of this paper is to provide a written report of the five part M&M project. Part one was sampling. We were to purchase 3 bags of M&M and record the color counts of each bag in an Excel spread sheet. For part two we calculated the sample proportions for each color, the mean number of candies per1. 69oz bag, created a histogram for the number of candies per bag, use Excel to compute the descriptive statistics for the total number of candies per bag and summarize the information.

In part three we located the 95% confidence interval for the proportion of blue, orange, green, yellow, red and brown. For part four we tested claims for percentages of each color. In the final part of the project we tested the hypothesis that the population proportions of red and brown were equal. This report will explain what was done, present the results and provide an analysis of what was found. 2 M & M Project Report Title This reported is presented on the statistical data investigated on M&Ms. This report contains information on the average number of candies per bag and sample roportions. We have conducted tests to ensure that our proportions, going into each bag of m&ms, are on target. We have also conducted hypothesis testing to ensure that our average number of m&ms per bag is on target as well. Project Part 1: Sampling Method The first assignment was to collect three 1. 69oz bags of plain M&Ms from different stores. We were to count each other color in each bag and record the information on a spread sheet in Excel. The students’ personal samplings were combined to create the full random sample. Project Part 2: Method, Analysis, Results

For this portion of the report we calculated the sample proportions for each color and the mean, or average number of candies per bag, number of candies per 1. 69oz bag. We also created a histogram for the number of candies per bag and summarized the total number of calculated proportions. The sample standard deviation was also calculated. A description of the histogram was provided along with the total number of candies sampled and the total number of bags sampled. The results are as follows: Sample proportions: blue=. 2366, orange= . 2099, green= . 1702, yellow= . 428, red= . 1156, brown= . 1249; the histogram is skewed left Mean= 55. 5667; standard deviation= 2. 0003; total # of candies=5001; # of bags= 90 The standard deviation indicates that the difference between the actual number of M&Ms per bag and the mean number of M&Ms per bag is 2. 0003. 3 M & M Project Report Part 3: Method, Analysis, Results The objective of this part of the project is was to construct a 95% confidence interval for the proportions of blue, orange, green, yellow, red and brown m&ms. The results were: Blue (. 22477, . 24833) Orange (. 19867, . 22125)

Green (. 15975, . 18058) Yellow (. 13308, . 15247) Red (. 10672, . 12444) Brown (. 11581, . 13414) Mean (55. 153338, 55. 979862 Bonus 438 Part 4: Method, Analysis, Results For this portion we were to tests Masterfoods’ claims about which proportion of colors the greatest number of people found attractive. Blue; H0: p=. 24 claim, H1: p . 24; Z= -. 5630, Fail to reject There is insufficient evidence to suggest the true proportion is not . 24. Orange; H0: p=. 20 claim, H1: p . 20; Z= 1. 75; Fail to reject There is insufficient evidence to suggest the true proportion is not . 0. Green; H0: p=. 16 claim, H1: p . 16; Z= 1. 9676; reject There is sufficient evidence to suggest the true proportion is not . 16. Yellow; H0: p=. 14 claim, H1: p . 14; Z= . 5706; Fail to reject There is insufficient evidence to suggest the true proportion is not . 14. Red; H0: p=. 13 claim, H1: p . 13; Z= -3. 0280; reject 4 M & M Project Report There is sufficient evidence to suggest the true proportion is not . 13. Brown; H0: p=. 13 claim, H1: p . 13; Z= -1. 0724; Fail to reject There is insufficient evidence to suggest the true proportion is not . 13.

Mean, H0: 54, H1: 54 claim; P= . 0000000014; reject There is sufficient evidence to support the claim that on average 1. 69oz bags will contain more than 54 candies. Bonus H0: 1. 5, H1: 1. 5 claim; = 113. 145; = 83. 71763, Fail to reject There is not enough evidence at the 5% level of significance to support the claim that the standard deviation number of candies is less than 1. 5. Part 5: Method, Analysis, Results For the final portion of our project we were instructed to test the hypothesis that the population proportions of red and brown are equal. Hypotheses= H0:p1=p, Ha: p1? p2; X1=578, n1=5001, p1=. 1156; X2=6235, n2=5001, p2= . 1250; = . 1203; Z= 1. 4447; = -1. 96 & 1. 96; z<-1. 96, z>1. 96 rejection region Fail to reject the null; There is not enough evidence to reject the claim. Quality Assurance To investigate one of the colors being off its targeted amount, I first inspect the settings on the machines to make sure that they had not been altered. If the setting on the bagging or mixing machine it will cause discrepancies in the proportions. Some of the m&ms may be spilling during the bagging process.

It is also possible that the machines may be malfunctioning. They may need to be serviced or replaced. It would be a good idea to check all equipment, so that m&m can maintain their standard of excellence. Conclusion 5 M & M Project Report The investigation into our product proportions yielded the expected results. The mean number of candies is more than 54. The color proportions are on target. The histogram gives us a visual of our results to make them easier to understand. Through these analyses we have learned that our product proportions are right on target. 6

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