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Kalliopi Karaiskos & Kelcee TaylorStatistics10/5/2015Final Project Each student was required to obtain a 2.17 oz. bag of Skittles. Each student then counted the total number of candies, as well as the total number of each color if candy, red, orange, yellow, green, purple. The class totals were then compiled in order to compare our won totals amongst out peers. The goal of the assignment is to help me, the student, conceptualize the ideas we are learning in class. We will learn to organize and analyze data, draw conclusions using confidence intervals and hypothesis tests, and use our critical thinking skills. Colors of Candy in each bag My DataClass DataYellow (23.53%)Yellow (18.45%)Purple (17.65%)Purple (19.65%)Red (17.65%)Red (18.85%)Green (17.65%)Green (20.39%) Orange (23.53%)Orange (22.66%)My most prevalent color of candy was both yellow and orange, with red, green, and purple all being second most. The graphs do reflect what I expected to see because there is just about an equal amount of each color. My data does vary from the class in a few ways, the class’s most prevalent color is only orange while mine is both yellow and orange. The orange were nearly the same in mine and the class. The class did have a higher percentage of red, green, and purple than I did, and the yellow was slightly lower than my percentage. Number of Candies per BagMean: 59.8 candies per bagStandard Deviation: 2.89Minimum: 53Q1: 59Median: 60Q3: 61.5Maximum: 68The shape of this data is not normal, although it does ascend to a maximum and then descend again. The graphs did show what I expected to see because there is not a lot variation in the number of candies per bag. Most bags fall within the normal range. My personal bag of candy had 68 candies in it, which is the maximum.Categorical data measures things that aren’t numbers, for example, colors or sizes. Quantitative data measures numbers, such s, number of candies, or heights of students. For categorical data, pie charts and Pareto are best, while box plots and stem and leaf plots would not make sense. Pie charts and Pareto charts make sense for this project because they show how prevalent one is over another without exact data. On the other hand, box plots and stem and leaf plots make sense for quantitative data, while pie charts and Pareto charts do not. Box plots and stem and leaf plots make sense for quantitative data because they use exact numbers. For categorical data, calculating the mode makes sense because it does not require any numbers, it only requires frequency. On the other hand, calculating median, mean, and range makes sense for quantitative data because actual numbers are being used. Confidence Interval Estimates:A confidence interval is a range of values whose purpose is to estimate the true value of a population perimeter. Confidence Interval Estimate for the true proportion of purple candies:95% confidence interval results:p : Proportion of successesMethod: Standard-WaldProportionCountTotalSample Prop.Std. Err.L. LimitU. Limitp29414960.196524060.0102737390.176387910.21666022We are 95% confident that the interval from 11.35 to 11.64 contains the true proportion of purple candies in Skittles bags. Confidence Interval Estimate for the true mean number of candies per bag.99% confidence interval results:μ : Mean of variableStandard deviation not specified.VariablenSample MeanStd. Err.L. LimitU. LimitTotal2559.440.4728636258.22198460.658016We are 99% confident that the interval from 63.81 candies to 64.19 candies contains the true population mean of number of candies per bag of Skittles. Confidence Interval Estimate for the standard deviation of number of candies per bag.98% confidence interval results:σ2?: Variance of variableVariableSample Var.DFL. LimitU. LimitTotal5.59243.121464912.357731We are 98% confident that the interval from 18.75 candies to 26.09 candies contains the true population standard deviation of candies in bags of Skittles. The purpose and meaning of a hypothesis test is to propose and idea that is out of the norm (HA) and then use statistical evidence to either reject or support it. Use a 0.01 significance level to test the claim that 20% of all Skittles candies are green:p : Proportion of successesH0?: p = 0.2HA?: p ≠ 0.2ProportionCountTotalSample Prop.Std. Err.Z-StatP-valuep30514960.203877010.0103417540.374888580.7077Reject the Claim that 20 percent of skittles in a bag are green. We reject Ho and accept HA Use a 0.05 significance level to test the claim that the mean number of candies in a bag of Skittles is 56:Hypothesis test results:μ : Mean of variableH0?: μ = 56HA?: μ ≠ 56VariableSample MeanStd. Err.DFT-StatP-value# of candies59.840.57930993246.6285761<0.0001Reject the claim that the mean number pf candies in a bag is 56Reflection:Completing this project has helped me understand how the same information can be presented in many different ways. Presenting the information in so many different ways helps me gain a more in depth understanding of the statistics being presented. As a Health Science major I will be reading medical journals and required to understand the findings. Having a deeper knowledge and understanding of statistics will help me interpret the information being presented to me. The ability to read and follow directions from a teacher and turn it into a project is a skill I was able to further develop throughout this project. It is an invaluable skill which I will continue to use not only through my schooling, but also in my career. In the beginning I had a difficult time understating the instructions and deciding what was being asked. In addition, I attempted to solve the problems by hand using the TI-84, which proved to be tedious and time consuming. I was able to overcome these challenges by utilizing problem solving skills. For example using the technology available to me, StatCrunch. I also chose to present problems I was experiencing to the teacher in order to receive help. Statistics has introduced me to more real-world applicable problems, as opposed to calculus or algebra. I find myself wondering about probabilities in my everyday life, for example when I submitted my application to Publishers Clearing House. I also was able to calculate the number of combinations possible when playing Clue with my family. Overall, I feel that statistics has been the most beneficial math class I have taken at Salt Lake Community College. The information is more applicable to real world situations, and therefore more useful. I have enjoyed seeing how information can be presented in so many different ways. Learning all the way numbers can be manipulated has been a great reminder to be skeptical when statistics are being presented to me. I have enjoyed this class and have learned a great deal of practical information. ................
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