Amanda and Marlee About Planet Smoothie! 3 rd Largest American Smoothie Company Founded 1995; Atlanta, GA Bonnie Rhinehardt President Franchise 16 States Doylestown, PA Description of Topic We went to Planet Smoothie in Doylestown! Recorded Size Money Spent Age Type of Smoothie Athlete/Non-Athlete Gender # Items Purchased We wanted to see if there was any association between the variables! Procedure Stood where people ordered/paid & recorded our data Collected data from every 3 rd person to order Tests: 1-Sample T-Interval Avg. $ Spent Test of Independence Gender v. Smoothie Size Test of Independence: Athlete v. Smoothie Type 1-Prop Z-Test: Amount of Regular Sized Smoothies 1-Sample T-Interval Amount of $ Spent 1.SRS 2. Normal population or n Population 10n Conditions Met T- Distribution 1- Sample T-Interval 1.Systematic Sample assumed random 2.N=70 n=30 3.The amount of people that go to Planet Smoothie is greater than 700 people 1-Sample T-Interval: Avg. Amount of $ Spent We are 95% confident that the average amount of money spent at Planet Smoothie is between $4.36 and $4.80. In repeated samples of 70 subjects, the confidence interval generated would capture the average amount spent 95% of the time. Test for Independence: Gender v. Smoothie Size We wanted to see if gender had any association with the size of smoothie purchased by Planet Smoothie customers. We removed Medium sized smoothies because not enough customers bought that size to run this test. Test for Independence: Gender v. Smoothie Size Categorical Data SRS All expected cell counts are greater or equal to 5 All conditions met x 2 test distribution x 2 test for independence Gender and Smoothie Size are categorical variables Stratified sample taken assumed random All expected cell counts greater than 5! H O : There is no association between gender and smoothie size. H A : There is an association between gender and smoothie size. Test for Independence: Gender v. Smoothie Size x 2 = P(df=1|x 2 > ) =.95 =.05 We fail to reject the H O because the P-value,.95, is greater than the alpha,.05. We have sufficient evidence that gender has no association with smoothie size purchased. Test for Independence #2: Athletes v. Type of Smoothie We also wanted to see if there was an association between customers that were athletes and the type of smoothie they chose. We narrowed it down to cool blended and energy because all of the other types had cell counts of less than 5. Also, this will show us whether or not athletes are conscious of the blast in their smoothie. We predict that the athletes would order energy smoothies more frequently! Test for Independence #2: Athletes v. Type of Smoothie Categorical SRS All expected cell counts greater than or equal to 5 Conditions met x2 distribution x2 test of independence Athletes & non-athletes and smoothie type are categorical We took a stratified sample assumed random All of our expected cell counts are greater than or equal to 5 Test of Independence #2: Athletes v. Type of Smoothie X 2 = P(df=1|x 2 >1.533)=.22 =.05 We fail to reject the HO because the P-value,.22, is greater than the alpha,.05. We have sufficient evidence that there is no association between athletes/non-athletes and their smoothie choice 1-Prop Z-Test : Amount of Regular Size Smoothies State SRS n n(1- ) 10 Pop 10n Check Systematic assumed random (.728)(70) (.271)(70) both greater than 10! Population of amount of regular smoothies bought is greater than 700! Conditions met normal model 1-prop z-test 1-Prop Z-Test Mechanics P(z>3.825) = x We reject the H O because the P-value, x 10 -5, is less than the alpha,.05. We have sufficient evidence that the proportion of regular smoothies sold is greater than.5, or 50%. Gender & Smoothie Choice Females 38/70 = 54.3% Protein: 0/38 = 0% Wellness: 12/38 = 31.6% Males 32/70 = 45.7% Cool blended: 13/32 Wellness: 2/32 = 6.3% Cool blended: 22/70 = 31.4% Favorite smoothie type among customers Energy: 20/70 = 28.6% Less customers were interested in the energy smoothies as a whole compared to cool blended smoothies Kids 9/70 = 12.9% There was a very small population of kids smoothies ordered between males and females. This may have been because there were not a lot of children collected in our sample. We conclude that more females came to PS than males. More females are concerned about their weight than males based on the statistics. The energy smoothie was fairly evenly distrubuted among males and females. Money Spent Right Skewed Unimodal Median : $4.39 IQR: $0.10 Range: $2.39-$9 Possible outlier at $2.39 Generally, the customers of PS paid around $4.39. Since the price of a regular happens to be $4.39, we can conclude that the majority of PS customers orders a regular sized smoothie. Items Bought v. Gender Female Right skewed Unimodal Gap Median: 1 IQR: 0 Range: 1-4 items Male Right skewed Unimodal Median: 1 IQR: 0 Range: 1-4 items The males and females have the same median, range, and IQR of number of items bought. From this we can conclude that the amount of items bought is not based upon the gender of the person purchasing the items. Athlete v. Size Non-A: 57/70 = 81.4% Non-A Kids: 12/57 = 21.2% Non-A Reg: 41/57= 71.9% Athletes: 13/70 = 18.6% A Kids 1/13 = 7.7% A Reg 10/13 = 76.9% Overall, more non-athletes got smoothies in general! Regular sizes were more often purchased between the non-as and athletes. From this graph, we can conclude that the customers of PS are more often non-as than athletes! Application If you were to walk into Planet Smoothie Most people in the building would buy a cool blended smoothie Most would also order a regular size An equal amount of males and females would be in there There would be more non-athletes than athletes You would expect to spend around $4.49 and purchase one item Bias & Error Only went to one PS Assumed age and athleticism Only 70 samples; couldve increased size Only went on the weekend rules out anyone that goes after work, school Holiday weekend! Misrecordings Customers buying for other people (not present) Some hours may have been busier than others Conclusion/Opinions We had fun! We thought more athletes would be there We eliminated blasts as a variableno one ordered them as additional items Not many people ordered more than just a smoothie Most of our predictions were correct Less males got wellness and weight loss smoothies For a better sample, we would change the days we went, especially since it was a holiday. Also, we would want to go on weekdays as well as weekends to vary our sample.