Report

How sweet of a deal are you really getting? By Kelly Culp, Ashley Hall, and Amanda Simo We wanted to research how many Sour Patch Kids were distributed in a bulk bag From there we wanted to see if the weight of the actual candies was equal to the claim on the package To do this we purchased bulk bags from both Costco and BJs We calculated the number, color, and weight of the Sour Patch Kids in each mini packet A BRIEF HISTORY ON THE LIFE OF SOUR PATCH KIDS Sour Patch Kids started as Mars Men – which were sold as one cent a piece The inspiration occurred during a time when UFO sighting were exciting Idea of a sour-coated soft candy with an “out of this world” tartness was developed in the late 1970s Believed that Frank Galatolie came up with idea of introducing sour products in soft confectionery category and experiment with cherry candy products New product was named Sour Patch Kids and distributed in the US in 1985 PROCEDURE In order to collect our data, we purchased bulk bags from Costco and BJs We took out the Swedish fish packets, and counted the Sour Patch Kids packets For each packet, we calculated the weight with a scale (in grams) We counted each color for the population of each bag, and the population of DISTRIBUTION OF COLORS Collection 1 Green Red 25% 24% Orange Yellow 25% 26% Green S1 = S2 = S3 = S4 = S5 = S6 = Red Orange Yellow 1.67857 1.63571 1.77143 1.64286 0 0 0 0 1 1 1 1 2 2 2 1.5 2 2 3 2 5 6 5 7 mean min Q1 median Q3 max Distribution of the population of sour patch colors remains very even. The means all colors fall within the 1.6-1.7 range. FREQUENCY HISTOGRAMS FOR COLORS Range: 0-5 Range: 0-5 Range: 0-7 Range: 0-6 Distributions are slightly right skewed and unimodal. Red and yellow colored sour patch have outliers. Yellow has a outlier of 7 and red has an outlier of 6. HISTOGRAM AND SCATTER PLOTS Our histograms show that the sour patch kids packets have a left skewed distribution, and are unimodal. Our range for the amount in each packet is from 010. Our scatter plot shows that the weight and amount of sour patch kids is linear. As the amount of sour patch kids in each packet increases, the weight of the packet increases. BOX PLOTS * These box plots appear similar because as we showed before, the amount and weight have a linear relationship. Our box plot shows that BJs appears to have a more even distribution of the amount of candies, and only two outliers. While Costco has 6 outliers. Costco has a greater range and smaller IQR, while BJs has a much large IQR but a smaller range. The weight of the candies appears to be slightly left skewed for both box plots between both stores. However, Costco has a smaller IQR, while BJs has a smaller range. CONCLUSIONS ABOUT OUR POPULATION Colors of the candies are evenly distributed The population of each color in each packet range from 0-7 Both yellow and red had outliers The distribution of the amount of candies is left skewed, and unimodal Mode = 8 Costco appears to have a lot more outliers and smaller IQR, but a greater range than BJs Costco’s distribution is more random ASSUMPTIONS FOR 1 SAMPLE T-TEST (TO SEE IF THE 15.0 CLAIM FITS) STATE 1) 2) 3) SRS Pop ≥ 10n Normal population or n ≥ 30 CHECK 1. 2. 3. Assumed representative Population of all Sour Patch Kids packets is greater than 1,400 140 ≥ 30 Conditions met → Student’s t-distribution → 1 sample t-test 1 SAMPLE T-TEST MECHANICS H 0 : 15 Collection 1 Weight 13.0724 g 3.6176 g S1 = mean S2 = s H A : 15 x 13.0724 – 15 t - 6.3041 = = 3 . 6176 / 140 s n 2 * P(t< -6.3041│df =139) = 3.5860 * 10-9 We reject the H0 because the p value of 3.5860 * 10-9 is less than alpha = .05. We have sufficient evidence that the true mean of the weight of sour patch kids per bag is not equal to15 grams. The stated weight on the outside of the bag incorrectly estimates the actual weight of the sour patch kids. CHI-SQUARE GOODNESS OF FIT TEST FOR COLOR STATE 1) 2) 3) CHECK Categorical Data SRS All expected counts ≥ 5 1) 2) 3) Yellow Colors are categorical Assumed representative All expected counts are greater than 5 Green Red Orange Observed 230 235 229 248 Expected 235.5 235.5 235.5 235.5 Conditions met → 2 distribution → 2 GOF test MECHANICS (observed expected) 2 (230 235.5) 2 (235 235.5) 2 x ... .9724 (expected) 235.5 235.5 2 p(x²›.9724│df=3)= .8079 We fail to reject the Ho because our p-value of .8079 is greater than = .05. We have sufficient evidence that the color Sour Patch Kids in the tiny packets are evenly distributed. 1 SAMPLE T-INTERVAL (95% CONFIDENCE) STATE 1) 2) 3) SRS Population ≥ 10n Normal population or n ≥ 30 CHECK 1) 2) 3) Assumed representative All Sour Patch Kids packets are greater than 1,400 Normal population displayed on graph Conditions met → Student’s t-distribution → 1 sample t-interval 1 SAMPLE T-INTERVAL MECHANICS x t * s 3.6176 = 13.0724 1.9772 = n 140 (12.468,13.677) We are 95% confident that the true mean of the weight of the bags of sour patch kids is between 12.468 and 13.677 grams. CHI-SQUARE HOMOGENEITY FOR COLOR VS. STORE STATE 1) 2) 3) CHECK Categorical Data SRS All expected counts ≥ 5 1) 2) 3) Conditions met → Colors are categorical Assumed representative All expected counts are greater than or equal to 5 2 distribution → Test for Homogeneity HYPOTHESIS Ho: The distribution of colors within the sour patch kids bags has no association to the store they were bought at. Ha: The distribution of colors within the sour patch kids bags has an association to the store they were bought at. df = 3 MECHANICS Yellow Green Red Orange BJs 108 (113.9) 127 (116.37) 109 (112.91) 121 (121.82) Cosco 122 (116.1) 108 (118.63) 119 (115.09) 125 124.18) (observed expected) 2 (108 113.9) 2 (127 116.37) 2 x ... 2.806 (expected) 113.9 116.37 2 p(x²›2.806│df=3)= .4225 We fail to reject the Ho because our p-value of .4225 is greater than = .05. We have sufficient evidence that the distribution of colors within the sour patch kids bags has no association to the store they were bought at. PERSONAL OPINIONS/ CONCLUSIONS The data was really hard to collect Tedious and Long Some were not full Sour Patch Kids so we had to use our judgment They are really good Had no problem eating them A mountain of Sour Patch Kids Should have purchased from a wide range of stores Hard to tell the true distribution, as some packaging of Sour Patch kids are sold differently Interesting experiment The distributions are fairly accurate The weight of the packets are below the stated weights APPLICATION When buying the packets of Sour Patch Kids, in the bulk size bags, you have a good chance of getting an even amount of each color HOWEVER, this is only if you go through each packet Some packets had 0 Sour Patch, and some had only one color! When buying Bulk Bags from Cosco, you are more likely to get outliers, meaning you have a greater chance of getting some with a lot of candies or very few Either way, the amount does not equal the 15 gram claim! BIAS / ERROR Human error When quickly counting the colors and weight we may have forgotten to zero the scale The weight of the sugar may have added, some bags had lots more sugar than others Only counted data from two stores: Cosco and BJs These are only one type of packaging, Sour Patch Candies come in all sorts of ways to buy These may have different distributions CONCLUSION The amount of Sour Patch Kids in each bag does not equal 15 grams, the expected interval is between 12.468 and 13.677 grams There is an even distribution between colors, when looking at the amount in all the packets The amount of candies in each packet is not evenly distributed Distribution is left skewed