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I Scream, You Scream, We All Scream for Ice Cream! Sarah Beeson, Jill Hall, Sarah Regan

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Cold Stone Creamery Founded in 1988 in Tempe, Arizona Uses in-store made ice cream that is combined with mix-ins, candy, and other toppings to create a new flavor Open year round Ice cream parlor chain

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Maggie Moo’s Founded in 1989 in Kansas City, Kansas 136 Treateries in 43 US states, Singapore, and Puerto Rico Specializes in ice cream and other desserts Independently owned and operated franchise stores

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Our Topic We set out to compare Cold Stone and Maggie Moo’s We went to two Cold Stone’s (Warrington and Willow Grove) and two Maggie Moo’s’ (Warrington and Landsale) Observed and surveyed for subject’s gender, order, price paid, size, preference, and frequency visited

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Procedure Observed customers in two of each store from May 27- 31 Allowed customer to order and surveyed every third customer to ensure randomness Used data table to record information

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Exploratory Data Analysis Seasonally is the most common ◦ With Sometimes close behind Frequently is the least common ◦ Possibly due to ice cream being seen as a seasonal treat Bar Graph of Frequency of Visits Frequently- 11.67% Sometimes- 31.67% Seasonally- 36.67% Almost Never- 20%

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Gender and Flavor With the exception of coffee and chocolate, flavors are fairly evenly distributed between gender Conclude gender has no effect on flavor Cake Batter- 50% female, 50% male Chocolate- 70% female, 30% male Coffee- 80% female, 20% male Mint- 55.56% female, 44.44% male Specialty- 62.5% female, 37.5% male Strawberry- 40% female, 60% male Vanilla- 54.54% female, 45.46% male

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Store Preference Cold Stone and Maggie Moo’s preference is approximately evenly distributed between the two We conclude that the population is evenly split on favorite store Cold Stone- 51.67% Maggie Moo’s- 48.33%

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Size Small and Medium are approximately evenly distributed ◦ Large has a much smaller frequency We conclude that the majority of the population orders small or medium Small- 40% Medium- 38.33% Large- 21.67%

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Price There are gaps between $3.50 and slightly less than $4.25, slightly above $4.25 and $4.50, and between approximately $5.12 and $5.30. We conclude that the average price paid is around $4.80 ◦ Size and amount of toppings affect price Histogram is right skewed. It spreads from $3.25 to $6.75. The center is $4.81.

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Gender and Preference Preference for store is approximately evenly distributed by each gender We conclude that gender and preference are not dependent Cold Stone: male- 38.71% female- 61.29% Maggie Moo’s: male- 41.38% female- 58.62%

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Data Analysis χ 2 GOF test for variety of flavors χ 2 test of homogeneity to compare size χ 2 test of independence for gender vs. store preferred

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x 2 GOF Test for Variety of Flavors Hypotheses ◦ Ho: Observed distribution of flavors fits the expected distribution of flavors ◦ Ha: Observed distribution of flavors does not fit the expected distribution of flavors Flavor cake batterchocolatecoffeemintspecialtystrawberryvanillatotal Frequency410591651160 Flavorcake batterchocolatecoffeemintspecialtystrawberryvanillatotal Frequency8.5714 60

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x 2 GOF Test for Variety of Flavors StateCheck 1. Categorical data 2. SRS 3. All expected counts ≥ 5 1. Flavor and frequency are both categorical 2. Assumed representative 3. 8.5714 ≥ 5 Conditions met x 2 distribution x 2 GOF test

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x 2 GOF Test for Variety of Flavors x 2 = 12.8 p=.0463 df=59 We reject the Ho because the p-value of.0464 is less than alpha=.05 We have sufficient evidence that the observed distribution of flavors does not fit the expected distribution of flavors

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x 2 Test for Homogeneity Hypotheses ◦ The distribution of sizes at Maggie Moo’s and Cold Stone is equal ◦ The distribution of sizes at Maggie Moo’s and Cold Stone is not equal

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x 2 Test for Homogeneity StateCheck 1. Categorical Data 2. SRS 3. All expected counts ≥ 5 1. Size and the store at are both categorical 2. Assumed representative 3. Counts are all above 5 Conditions met x 2 distribution x 2 test for homogeneity

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x 2 Test for Homogeneity x 2 = 34.74 p= 2.8596x10 -8 df= 2 We reject the Ho because the p-value of 2.8596x10 -8 is less that alpha=.05. We have sufficient evidence that the distribution of sizes ordered at Cold Stone and Maggie Moo’s is not equal.

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x 2 Test for Independence Hypotheses ◦ Gender and preference are independent of each other ◦ Gender and preference are dependent on each other

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x 2 Test for Independence StateCheck 1. Categorical Data 2. SRS 3. All expected counts ≥ 5 1. Gender and preference are categorical 2. Assumed representative 3. Counts are all above 5 Conditions met x 2 distribution x 2 test for independence

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x 2 Test for Independence x 2 =.04449 p=.83 df= 1 We fail to reject the Ho because the p-value of.83 is greater than alpha=.05. We have sufficient evidence that gender and preference for Cold Stone and Maggie Moo’s are dependent variables.

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Conclusions from Tests χ 2 GOF test for variety of flavors ◦ Observed distribution of flavors does not fit the expected distribution of flavors χ 2 test of homogeneity to compare size ◦ Distribution of sizes ordered at Cold Stone and Maggie Moo’s is not equal χ 2 test of independence for gender vs. store preferred ◦ Gender and preference for Cold Stone and Maggie Moo’s are dependent variables

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Bias and Error Undercoverage ◦ Only surveyed 4 stores in the area; other areas may be different Time of day/ year ◦ Different times of day would get different responses Number of toppings ◦ Large numbers of toppings affect price

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Personal Opinions and Conclusions Preference for store was basically evenly distributed between subjects ◦ Preference broken down by gender was also even Project took a lot of time and effort ◦ More time would have allowed for better data collection

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