Ice Cream Melting Times Emma Hutchinson Marianna Ator

Introduction Summer is near/here and that means one thing. ICE CREAM. Ice cream is possibly one of the greatest food creations of all time. But there is one large problem with ice cream and that is of course, how fast it melts. So we decided to see whether a person should shell out more money just to ensure that their ice cream melted slower and they could enjoy that yummy goodness in peace. We decided to compare two brands of Vanilla ice cream, Giant Brand, a generic brand which is the cheapest kind to buy at Giant grocery stores, and Häagen-Dazs, the most expensive brand of ice cream at Giant grocery stores. To give you some perspective, Giant Brand full-fat Vanilla ice cream costs $4.29 for a 1.75 Quart container, Häagen-Dazs costs $6.79 for a 1 pint container. This difference is a pretty significant one if you are a person who likes to eat a lot of ice cream. To make sure our melting times were normal we also had a control ice cream that we melted with was Edy’s brand. Edy’s comes in at $5.79 for a 1.75 Quart container, making it in between the two brands we were testing. We know that certain brands of ice cream are more expensive because of taste but in this case we wanted to know what a person should do if they only care about how long they have to eat their ice cream before it gets all over them.

Hypothesis The hypothesis we are testing is the idea that the more expensive the ice cream, the longer it will take to melt. Therefore the more expensive the ice cream the lower the melting mean. Ho: There is no difference between the mean melting time of Giant brand ice cream and the mean melting time Häagen-Dazs ice cream. Ha: The mean melting time of Häagen-Dazs ice cream is lower than the mean melting time of Giant brand ice cream.

Materials 10- 1.75 Quart containers of Edy's Grand Ice Cream Vanilla ice cream 10- 1.75 Quart containers of Giant Brand Vanilla Ice Cream 10- 1 Pint containers of Haagen-Dazs Ice Cream Vanilla ice cream 3- 12 oz. ceramic bowls of the same set 1- 1 cup measuring cup 1- Timer with a minute and second hand 3- labels labeled A, B, C with the actual brands hidden underneath

Procedure We went to three different grocery stores to purchase containers of ice cream to ensure randomization. At each store we bought three containers (except at one store where we bought 4 of each) of each kind of ice cream (Giant Brand, Häagen-Dazs, and Edy’s) to total 10 containers of each type of ice cream. To make sure our results were not completely random we chose to measure Edy’s melting time as a control because it was between Giant and Häagen-Dazs in price. Next we took all the ice cream and put it in a freezer together for one night (16 hours) to make sure all the ice cream containers were all at the same temperature level. We then, took exactly one cup of each type of ice cream and put them each in a separate bowl. All of the bowls were the same material ensuring that this could not be a factor in melting time. We put the bowls on a counter inside where the temperature was 78 degrees Fahrenheit. To make sure that we were not biased we had a third party make labels that said A, B, and C. The third party then arranged the ice cream while we were in the other room, writing what brand the ice cream was on the bottom of the label. We then used a timer on a watch to see how long each ice cream took to melt. We waited until the ice cream was melted all the way through, without any clumps, to announce that it was melted. After our first trial we repeated steps 3 through 6 using a different container of ice cream for each bowl. Following the 1st trial we did the experiment with three bowls of each type of ice cream at one time (3 one cup bowls of Giant, Häagen-Dazs, and Edy’s) in order to prevent having to resume on the next day when the temperature inside might have been different.

Data Average Melting Time (in minutes) Giant Häagen-Dazs Edy’s (Control) 63 74 66 77 72 68 73 64 61 69 80 67 81 58 75 60 57 78 65

What Test to Use We will perform a two-sample t test because of how small the samples are. Assumptions: Independence- We purchased the ice cream containers separate from one another (different stores) Random- We purchased the ice cream random from each other Nearly normal- The melting times are nearly normal when compared in a histogram

Calculations Giant Brand: x= 62.7 Sx= 3.713339318 Häagen-Dazs: x= 75.4 Sx= 4.501851471 T- VALUE: √(3.713339318)2 + (4.501851471)2 10 10 = 1.845414738 62.7-75.4 = -6.881921845 1.845414738 P-VALUE= 1-.00000009747= .9999990253

Analysis & Conclusion Since our p-value is so high at .9999990253 we have no sufficient evidence to reject Ho at most significance levels. This means that we cannot reject the idea that the Giant brand ice cream melts at the same rate as the Häagen-Dazs ice cream. Therefore, if someone wanted to buy ice cream solely on the amount of time it took to melt, it doesn’t necessarily pay to purchase the more expensive brand.