The Adventures of the Swiss Miss Marshmallows By Skyler Northcutt & Vivian Skumpija

Description of Project We planned to research how many marshmallows are packaged in one packet of Swiss Miss Hot Chocolate with marshmallows. – See how the amount of marshmallows was distributed per packet We surveyed a total of 100 people at Wegmans to find out their preference in relation to drinking hot chocolate with or without marshmallows – Charted their gender, age group, and preference – Did this in order to randomize our voluntary response sample

Swiss Miss Hot Chocolate Sold by an American Food Company, ConAgra Foods Inc. Available In: – regular and "no sugar added“ – with or without small marshmallows – Great Start Cocoa (fortified with 15 essential vitamins and minerals) – Pick-Me-Up (with 67 mg of caffeine/packet) For over 20 years, Swiss Miss sales remained at about 40% of national cocoa mix sales for many years

Procedure 1.At Wegmans, over a total of 4 hours, we approached every fifth person to come out of the store. a.Made sure to survey people at various times of the day b.Wanted to get voluntary responses from people 2.After the survey, we went on to test our numerical data

Procedure (cont.) a.Bought 4 boxes of Swiss Miss Hot Chocolate with Marshmallows from 3 different grocery stores (Genaurdis, Acme, Wegmans) b.Each box had 10 packets, resulting in 40 samples from each store, increasing our sample size c.In their store grouping, we opened the packets and sifted through the hot chocolate in order to count all the marshmallows in one packet. d.We repeated this process for each of the 40 packets from the different stores.

Marshmallow Count: Genaurdis Histogram: Unimodal, roughly symmetric, (8,28), center roughly at 17 Normal Quartile Plot: Strong and Linear= normal model Only whole numbers

Marshmallow Count: Genaurdis

Marshmallow Count: Acme Histogram: One mode with numerous peaks, slightly right skewed, (8,27), center roughly at 15, gap Normal Quartile Plot: Strong and Linear= normal model Only whole numbers

Marshmallow Count: Acme

Marshmallow Count: Wegmans Histogram: Unimodal, roughly left skewed, (6,29), center roughly at 16, outlier at 29 Normal Quartile Plot: Strong and Linear= normal model Outlier Only whole numbers

Marshmallow Count: Wegmans

Marshmallow Count: All Together

Survey: Age Group & Age Group with Preference Key: A- Adult, E- Elderly, K-Kid, T-Teen Majority of adults and elderly surveyed Most people prefer marshmallows in their hot chocolate

Survey: Gender & Gender with Preference Key: F-Female M-Male Majority of females surveyed Most people prefer marshmallows in their hot chocolate

T-Intervals Of Marshmallow Count Conditions 1.SRS 2.Pop >10n 3.Normal population or > 30 1.Randomized sampling 2.There are more than 400 packets of Swiss Miss Hot Chocolate; there are more than 1200 packets also 3.40 > 30, 120 >30 All conditions met, Students’ t model, 1sampTinterval Df= 39, Df= 119

1SampTInterval: Genaurdis Marshmallows per packet We are 95% confident that the true mean of marshmallows per packet from Genaurdis is between and marshmallows.

1SampTInterval: Acme Marshmallows per packet We are 95% confident that the true mean of marshmallows per packet from Acme is between and marshmallows.

1SampTInterval: Wegmans Marshmallows per packet We are 95% confident that the true mean of marshmallows per packet from Wegmans is between and marshmallows.

1SampTInterval: All Together Marshmallows per packet We are 95% confident that the true mean of marshmallows per packet from all three stores combined is between and marshmallows.

Chi-Square Test for Gender and Marshmallow Preference Goodness of Fit DF= 1 Conditions 1.Categorical Data 2.SRS 3.All expected counts > 5 1.Gender and Preference are categorical 2.Random 100 people survey sample 3.All expected counts > 5

Chi-Square Test for Gender and Marshmallow Preference Ho: there is not an association between gender and marshmallow preference Ha: there is an association between gender and marshmallow preference (10-12)²+ (9-7)²+…= P( >1.082|DF=1) =.2982 We fail to reject the Ho because the p-value.2982 > alpha =.05. We have sufficient evidence that there is no association between gender and marshmallow preference.

Chi-Square Test for Age Group and Marshmallow Preference Goodness of Fit DF= 3 Conditions 1.Categorical Data 2.SRS 3.All expected counts > 5 1.Age group and Preference are categorical 2.Random 100 people survey sample 3.All expected counts > 5 (except 2)

Chi-Square Test for Age Group and Marshmallow Preference Ho: there is not an association between age group and marshmallow preference Ha: there is an association between age group and marshmallow preference (7- 6.8)²+ (8- 6.7)²+…= P( >.9148|DF=3) =.8219 We fail to reject the Ho because the p-value.8219 > alpha =.05. We have sufficient evidence that there is no association between age group and marshmallow preference.

Concluding… Through the intervals, we found that all together, the average mean of marshmallows per packet from Swiss Miss is between and marshmallows. Our Chi-Square tests revealed that both gender and age group have no association to drinking hot chocolate with or without marshmallows.

Application to Population Majority of Bucks County residents prefer marshmallows in their Hot Chocolate – Their age and gender remains independent from this preference. Swiss Miss Hot Chocolate sold in Genaurdis, Acme, and Wegmans in Bucks County all appeared to have randomized marshmallow quantities per packet, having similar intervals.

Bias and Error A person missed at Wegmans during the survey People who chose not to answer, voluntary response Wrong estimation of age group Difference in counting certain marshmallows – Broken pieces or conjoined Could have… – Increased sample size – Avoided voluntary response bias some how – Gone to different places besides Wegmans

Personal Opinions Skyler : It was awkward approaching some of the people at Wegmans because they didn’t take me seriously. Sifting was a blast! Vivian : Unique process with a sifter and massive amounts of hot chocolate powder up my nostrils, my mom zip lock bagged them to save them for later consumption