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Math and Cookies

As many of you know, for my end of the year statistics project, I tested different types of flour in cookies to see which one people liked the most. This was the most fun I’ve had with a project well…in all four years of high school. Better late than never I suppose…

Question: What type of flour makes the tastiest chocolate chip cookie?

H0: People find chocolate chip cookies made with any type of flour to be equally tasty.

HA: People find chocolate chip cookies with made with one flour to be tastier than the rest.
Martha Stewart’s “Soft and Chewy Chocolate Chip Cookies”

  • 2 1/4 cups all-purpose flour
  • 1/2 teaspoon baking soda
  • 1 cup (2 sticks) unsalted butter, room temperature
  • 1/2 cup granulated sugar
  • 1 cup packed light-brown sugar
  • 1 teaspoon salt
  • 2 teaspoons pure vanilla extract
  • 2 large eggs
  • 2 cups (about 12 ounces) semisweet and/or milk chocolate chips
  • Bake @ 350° for ≈ 9 minutes

Alton Brown’s “The Chewy”

  • 2 sticks unsalted butter
  • 2 1/4 cups bread flour
  • 1 teaspoon kosher salt
  • 1 teaspoon baking soda
  • 1/4 cup sugar
  • 1 1/4 cups brown sugar
  • 1 egg
  • 1 egg yolk
  • 2 tablespoons milk
  • 1 1/2 teaspoons vanilla extract
  • 2 cups semisweet chocolate chips
  • Bake @ 375° for ≈ 9 minutes

Alton Brown’s “The Puffy”
  • 1 cup butter-flavored shortening
  • 3/4 cup sugar
  • 1 cup brown sugar
  • 2 1/4 cups cake flour
  • 1 teaspoon kosher salt
  • 1 1/2 teaspoons baking powder
  • 2 eggs
  • 1 1/2 teaspoons vanilla extract
  • 2 cups semisweet chocolate chips
  • Bake @ 375° for ≈ 9 minutes

Joy the Baker’s “Whole Wheat Chocolate Chip Cookie Dough”

  • 2 1/4 cups whole wheat flour
  • 1 teaspoon salt
  • 1 teaspoon baking soda
  • 1 cup brown sugar, firmly packed
  • 1/2 cup granulated sugar
  • 1 cup unsalted butter, softened
  • 1 teaspoon vanilla extract
  • 2 eggs
  • 2 cups semi sweet chocolate chips
  • Bake @ 350° for ≈ 9 minutes

Phew, making all those cookies was quite tedious but carrying out the experiment was definitely the most rewarding. Each person taking part in the experiment would try all 4 cookies (without knowing which one they were tasting obviously!) and they would rate them 1-4 collectively with a rating of 1 being the best. I also asked them what their cookie preference was i.e. chewy, thin, cakey, crunchy, etc.
They were all pretty excited to be getting cookies…
…Some more than others
After counting up all the results, here is the raw data:
In order to test whether I would reject or fail to reject my null hypothesis, I had to perform a Chi Square Goodness of Fit test which means I had to subtract my expected count (which was 16.75 because 67 people took part in my experiment, there were 4 cookies, 67/4=16.75 blahblahblah…) from my observed count, square it, and then divide by my expected count. I know, I know. I hate math too but here it is:
My significance level was .05 and I had 3 degrees of freedom because there were 4 cookies so after I entered that into my calculator, my p-value was . 00016615391. Therefore, because it was so small, at a α= .05, the probability of all four cookies being rated equally in “tastiness” (16.75 voting each cookie #1) is less than.01%. Therefore, I reject my null hypothesis that people like chocolate chip cookies made with any type of flour to be equally tasty in favor that people find chocolate chip cookies made with one type of flour to be the tastiest over the rest. And now we know that flour is bread flour! I personally believe it was because bread flour has the most gluten in it, giving it the chewiest texture.

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