Notes

We first defined our two parameters as
Mu sub-G is the average rating people assigned to the survey with an appealing image of pineapple pizza give to the taste of pineapple on pizza.

And Mu sub-B is the average rating people assigned to the survey with an unappealing image of pineapple pizza give to the taste of pineapple on pizza.

The null hypothesis is that the average rating of the taste of pineapple pizza is the same for both treatment groups, those being the group shown an appealing image of pineapple pizza and the group shown an unappealing image.

The alternative hypothesis is the average rating of the taste of pineapple pizza of the group shown an appealing image of pineapple pizza is greater than that of the group shown an unappealing image of pineapple pizza.

There are two validity conditions that we needed to meet: independence and normal sampling distribution. Since our population was strictly defined as Northside College Prep juniors, we concluded that we did use random sampling. For independence, our sample was greater than 10% of the population. Our sample size of 37 is 18.5% of the population of about 200. The data was not normally distributed, and we failed to pass the threshold for sample size, which we defined at 20. For the group given the unappealing photo, the sample size was 14 and for the group given the appealing photo, the sample size was 23. Since 14 is less than 20, we failed to meet the condition for a normal sampling distribution. Since we failed to meet both conditions, the results of our experiment should be analyzed and interpreted with higher scrutiny.

As for the mathematical process, We decided to use a two-sample T-test for a difference between two population means since we are dealing with quantitative data. We compiled two lists, which contained the data we derived from our surveys, in a TI-84 calculator to derive our sample means (which were 2.857 for the group shown an unappealing image and 3.261 for the group shown an appealing image) and standard errors (which were 1.3557 for the group shown an appealing image and 1.46 for the group shown an unappealing image, which we plugged into the equation for a t-statistic. We ended up getting a t-statistic of 0.838, degrees of freedom of 25.994 derived from the calculator's 2-sample t-test, which would correspond to a p-value of 0.201.