# M & M Project

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• Published : November 24, 2011

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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. 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 proportions. 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= .1428, 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.

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[pic] .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[pic].20; Z= 1.75; Fail to reject There is insufficient evidence to suggest the true proportion is not .20.

Green; H0: p=.16 claim, H1: p[pic] .16; Z= 1.9676; reject
There is sufficient evidence to suggest the true proportion is not .16.

Yellow; H0: p=.14 claim, H1: p[pic] .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[pic] .13; Z= -3.0280; reject
There is sufficient evidence to suggest the true proportion is not .13.

Brown; H0: p=.13 claim, H1: p[pic] .13; Z= -1.0724; Fail to reject There is insufficient evidence to suggest the true proportion is not .13.

Mean, H0: [pic] [pic]54,...