Report

By: John Marron Nicole Scamuffo • Distribution of color • Time it takes to dissolve: –warm vs. cold water –stirring vs. not stirring • Originally produced by Jolly Rancher Company – Founded in 1949 by Bill and Dorothy Harmsen • Sold to Beatrice Foods in 1966 • Purchased by Leaf Candy Company in 1983 • 1996 Hershey bought the Jolly Rancher Candy Company • We used the “original” Jolly Rancher which contain 5 flavors: Blue Raspberry Cherry Grape Green Apple Watermelon • 1 bag of Jolly Ranchers from 3 stores = 3 bags – Each bag is estimated to have 66 hard candies – Claimed that the colors are evenly distributed within bags • Grouped colors together from all 3 bags 50 45 40 35 30 Genuardi's 25 Wegmans Target 20 15 10 5 0 Color Distribution Purple Red Green Pink Blue • Larger overall total: – Red and blue • Smallest overall total: – Purple • Green and pink have around same count • Different stores have different amounts • Based off of this data we feel; – Jolly Rancher company doesn’t fill the bags evenly STATE • SRS • All expected counts ≥5 CHECK • assumed • All expected counts ≥5 • Ho: the observed frequency distribution of Jolly Rancher color fits the expected distribution • Ha: the observed frequency distribution of Jolly Rancher color doesn’t fit the expected distribution P(x2> 1.0456 Idf =4) = 0.903 • We fail to reject Ho because the p-value >α= 0.05 • We have sufficient evidence that the observed frequency distribution of Jolly Rancher color fits the expected distribution 1. Determine whether candy dissolves faster in hot water or cold water – Heated up half in the microwave for 5 minutes and refrigerated other half 2. Place 50 jolly ranchers into plastic cups that hold ¼ cup of warm water 3. Place 50 jolly ranchers into plastic cups that hold ¼ cup of cold water – Used calc for random sample 4. Record the amount of time it takes for each jolly rancher to dissolve in the water 5. Perform a 2 sample ttest Box Plot Jolly Rancher Jolly Rancher hot_w ate r_not_s tirring 38.969 22.67 35.22 40.69 42.43 50.5 7.21 20 25 30 35 40 45 hot_w ater_not_stirring 50 55 S1 S2 S3 S4 S5 S6 S7 = = = = = = = mean min Q1 median Q3 max iqr Jolly Rancher Box Plot Jolly Rancher cold_w ate r_not_s tirring 75.0384 61.4 71.91 74.29 76.23 87.46 4.32 60 65 70 75 80 cold_w ater_not_stirring 85 90 S1 S2 S3 S4 S5 S6 S7 = = = = = = = mean min Q1 median Q3 max iqr • As you can see in the two box plots: Hot water: Minimum: 22.69 –outlier Maximum: 50.5 Mean: 30.97 Q1: 35.22 Q3: 42.43 IQR: 7.21 Cold water: Minimum: 61.4 –outlier Maximum: 87.46—outlier Mean: 75.04 Q1: 71.91 Q3: 76.23 IQR: 4.32 ** cold water seemed to •Hot water graph is left skewed have a lot of outliers •Cold water graph is symmetric •Based off of the graphs , we believe that it takes longer for a Jolly Rancher to dissolve in cold water than it take for one to dissolve in warm water STATE • 2 independent SRS • 2 normal pops or n1 and n2 ≥ 30 • S1= S2 CHECK • Assumed • n1 and n2 ≥ 30 N1 = 50 N2 = 50 • 5.6 = 5.1 Ho: µw = µc Ha: µw < µc P(t> -33.44 I df = 98 ) = < 0.0001 • We reject Ho because the p-value is < α= 0.05. • We have sufficient evidence that the mean of dissolving a Jolly Rancher in warm water is less than the mean of dissolving a Jolly Rancher in cold water 1. Heated up water for 5 minutes 2. Placed ¼ cup of water into 30 plastic cups containing 1 Jolly Rancher 3. Stirred water with a plastic knife until J.R dissolved 4. Recorded times 5. Perform 2 sample t-test to determine if stirring has an effect on the amount of time the candy took to dissolve – reused warm water data Jolly Rancher Box Plot Jolly Rancher Stirring_in_w arm _w ater 23.5303 18.04 21.66 23.975 25.6 27.59 3.94 18 20 22 24 Stirring_in_w arm _w ater 26 28 Box Plot Jolly Rancher S1 S2 S3 S4 S5 S6 S7 = = = = = = = mean min Q1 median Q3 max iqr Jolly Rancher hot_w ate r_not_s tirring 38.969 22.67 35.22 40.69 42.43 50.5 7.21 20 25 30 35 40 45 hot_w ater_not_stirring 50 55 S1 S2 S3 S4 S5 S6 S7 = = = = = = = mean min Q1 median Q3 max iqr • The graphs show that: Hot water: Minimum: 22.69 –outlier Maximum: 50.5 Mean: 30.97 Q1: 35.22 Q3: 42.43 IQR: 7.21 Hot water + stirring: Minimum: 18.04 Maximum: 27.59 Mean: 23.53 Q1: 21.66 Q3: 25.6 IQR: 3.94 • Both graphs are left skewed – Stirring = more clustered and a more extreme skew • Based off of the data we feel that a Jolly Rancher will dissolve faster in warm water while being stirred rather than just sitting in the warm water STATE • 2 independent SRS CHECK • Assumed • 2 normal pops or • n1 and n2 ≥ 30 • n1 and n2 ≥ 30 • N1 = 50 • N2 = 30 Ho: µw = µs Ha: µw > µs = -16.57 P(t> -16.57 I df = 73.469 ) = < 0.0001 • We reject Ho because the p- value is < α= 0.05. • We have sufficient evidence that the mean of dissolving a Jolly Rancher in warm water without stirring is greater than the mean of dissolving a Jolly Rancher in warm water while stirring • Applies to people who purchase Jolly Ranchers – Getting a good deal—colors seem to be equally distributed • Melt faster in a warm environment (mouth) • 1st study– only took bags from Buck County area – Most likely same distribution center • 2nd test– water temperature changed as it sat – Both ended up at room temp • 3rd test– different stirring techniques • Too much work to do in too little time – Not every store had Jolly Ranchers • Jolly Ranchers took too long to dissolve – Cold water took over an hour • Surprised at the time difference between the temperature waters