Bag RED ORANGE GREEN YELLOW PURPLE Candies per Bag

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1 Skittles Project For this project our entire class when out and bought a standard 2.17 ounce bag of skittles. Before we ate them, we recorded all of our data, the amount of skittles in our bag and the proportion of each color in the bag. We then complied all of our data into a large sample so we could compare our data to the class s. We are trying to figure out what the proportion of each color is in each bag of skittles. The class sample data will be compared to our own bag individual bag of skittles to see if there is a difference from the average amount of skittles in each bag, the color of each in every bag and how that compares to a single bag. The data below is all of the collective data from the class. The chart is each individual bag broken down by color and the number of candies in each bag. The average bag number of candies in the bag is 60 candies and for the most part each color is evenly distributed across the board. This is what I expected to see from the data, my personal data is a little more skewed than the collective data but it is fairly similar. With the average number of candies being 60 in each bag and my bag had 55, that is lower than what I would have expected but it isn t too unusual. Class Data: 330 Red Green Yellow Orange Puprle Purple Yellow Green Orange Red % 18% % 20% 270 Color of Skittles 21%

2 Bag RED ORANGE GREEN YELLOW PURPLE Candies per Bag Column Totals

3 Personal Data: Personal Bag Purple Green Yellow Orange Red 11% % 16% % 20% 0 RED YELLOW ORANGE GREEN PURPLE Bag RED ORANGE GREEN YELLOW PURPLE Candies per Bag Proportion Below are the graphs of quantitate data, data that can be counted. In this section we won t be looking at things such as color and focus of number of candies in each bag and how they compare to each other. The distribution of the candies are normally distributed, such as I had expected but the class data does differ from my personal data. Since I had a bag that contained only 55 candies my bag is considered to be on of the four outliers in the collective data set. Five Number Summary Minimum Value Quartile 1 Mean Quartile 3 Max Value

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5 In reflection to this part of the assignment, the data that we have calculated is fairly close to what I had expected to see. The data is normally distributed, there are more outliers than I would have expected but for the most part it is pretty normal. A Pareto Chart and Pie Chart are the easiest graphs to use when showing categorical data simply because the show the proportion of each color very easily and clearly. A histogram wouldn t work for categorical data because the numerical data is along the x-axis of the graph which would make it impossible to show categorical data across that axis. Part 2 This next part of the project we will be looking at confidence intervals. I will construct three different confidence intervals with the given skittles data, the intervals show how accurate a study is. For example, the first confidence interval that we will be constructing is looking at the proportion of yellow candies to the whole bag. I will construct it with 99% confidence that the true proportion of yellow skittles in each bag is what I say it is, given a little bit of wiggle room, about one percent, which is the remaining percent taken out of 100. I conducted 3 different confidence intervals, one about the percentage of yellow skittles in each bag, the mean number of skittles in each bag and the standard deviation of skittles in each bag. The first calculation shows that in all of the candies in the world I am 99% sure that there is between 17.6% and 23% of candies are going to be yellow in any given bag of skittles. The second calculation shows that I m 95% sure that the mean, or average, number of candies in each bag is between 58.6 and 62.2 candies in each bag. The final calculation shows the standard deviation of the number of candies in each bag. This is saying that since there is an average, lets say 60 candies it would not be surprising if there were plus or minus about 5 candies in each bag. For the hypothesis testing the first calculation shows that we didn t reject the null hypothesis which is saying that there isn t enough evidence for us to deny the fact that there is a 20% of the candies in each bag are going to be red. The second hypothesis test is asking if there is a 99% chance that all of the bags of skittles have 55 candies in each of them. In this process we were able to reject our claim therefore saying I am not confident that 99% of all skittles bags have 55 candies in them. For each of these tests their are certain requirements to make sure that these tests are accurate. For each of the tests they must be from a simple random sample, in needs to be a binomial distribution, and for proportions, you must have at least five successes and five failures. Meaning that there needs to be at least five red candies and five other candies. For the second hypothesis test we did it has to be normally distributed, taken from a simple random sample, and be a binomial distribution. These processes were eye opening to me. I was surprised by a lot of the results that we received from the calculations made in the project. From this section we learned that all of the colors of skittles in each bag of candies is fairly close to even with a little bit of an error involved.

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8 Nick Rowley Prof. Brenda Santistevan 12/2/14 Skittles Reflection I really enjoyed doing this Skittles project, I learned many valuable lessons during this project and am glad that I had the opportunity to do it. In the project we did many different equations and developed graphs and charts to show the relationship of the class and our own personal bag of skittles. The first part of the project we did we found the proportion of all of the color of skittles in our bag. Everyone in the class did this and we all submitted our data onto a spreadsheet so we could easily compare and contrast them to each others bags. This is the first time that I was able to put the concepts I had learned into real world situations. When I first started this project I figured that, for the most part, each Skittle color in the bag would be fairly evenly distributed. As I had predicted, they were. Another thing that I had learned from doing this project is that from a sample of data, as long as it is a simple random sample, you are able to predict about the correct proportion for a population. Meaning that with my bag of skittles that I had purchased I was able to predict about the average proportion of each color of candies in every bag in the history of the world. Granted it wouldn t be completely accurate but we can get a prediction that is close enough we could be able to use it. In conclusion, as I had stated earlier I am glad that I had the opportunity to do this project and take this class. This has shown me how to use the principles that we learned in class and how to use them in real life situations.

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