Running head: M&M PROJECT REPORT
This paper examines the proportion of M&M candies through the random sampling of 156 bags. After reading this paper one should have a better understanding of the process that accompanies packaging M&M candies. The bags used in the experiments were taken from different stores to help ensure a true sample of all the 1.69 oz of plain M&M candies.
Introduction: Purpose of Report
The purpose of this report is to examine the five project parts of an M&M analysis and examine a method for quality control. The parts of this project included using random sampling to gather data on the number of colored M&M candies, the sample ...view middle of the document...
Project Part 2: Method, Analysis, Results
The second portion of the project was based on the combined data set. The results showed a total of 156 bags sampled with a total of 1849 blue, 1944 orange, 1614 green, 1083 yellow, 1154 red, and 1093 brown candies. The total number of candies sampled equaled 8713 M&Ms. From this information the sample proportion and the sample mean were collected. The sample proportion was found by add up each column of candies and dividing by the total number of candies. For example, take the 1849 blue candies and divide them by the total candies 8713 and you get a sample proportion of 0.2122. Next we calculated the sample mean by dividing the total numbers candies by the total number of candy bags for a sample mean of 55.85. All this information was saved under the data tab of excel project.
Next another excel sheet was created to show a histogram for the number of candies per bag. The histogram shows the frequency distribution in a data set. This histogram also showed the bin which represents how to group the data into classes for graphing. According to the histogram a bag that contains 45 candies is a possible outlier; an outlier is data that lies outside the normal range. Opening another excel sheet the descriptive statistic was computed. The descriptive statistic displayed the mean, standard error, median, mode, standard deviation, sample variance, range, minimum, maximum, sum, and count. The last excel sheet contained a summary statistics which showed the numbers of each colored candy, the sample proportion for each colored candy, the sample mean of candies per bag, the sample standard deviation of mean number of candies per bag, written description on the histogram, and sample size.
Project Part 3: Method, Analysis, Results
For part three of the M&M project a 95% confidence interval for the proportion of each colored M&M candies was constructed. A confidence interval represents the “estimate of a population parameter (Larson, & Farber, 2009).”In order to construct the confidence interval the margin of error is needed, this formula is as followed . To find z we look up confidence interval for 95 and find that it is 1.96. The is the sample proportion of the color for example 0.2122 for blue candies. The is found by doing 1 - , so keeping with the blue candies 1-0.2122=0.7878. Lastly the n is the total number of candies sampled which is 8713. When the values are plugged into the margin of error equals 0.008585.