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AP Stats Inference Test ANOVA

AP Stats Inference Test ANOVA. Jordan Mahoney Raphael Schuster Daniel Kaplan. Set Up. Do McDonalds, Burger King, and Wendy’s have the same mean number of fries in a small order? µ m = true mean number of fries per small order at McDonalds

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AP Stats Inference Test ANOVA

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  1. AP Stats Inference Test ANOVA Jordan Mahoney Raphael Schuster Daniel Kaplan

  2. Set Up • Do McDonalds, Burger King, and Wendy’s have the same mean number of fries in a small order? • µm = true mean number of fries per small order at McDonalds • µw= true mean number of fries per small order at Wendy’s • µB= true mean number of fries per small order at Burger King • H0: µm = µw = µb • Ha: At least one of the means is different

  3. Methodology • We went to three fast food restaurants at the same time of day and ordered 5 fries from them at the same time. • We carried out this experiment to see which fast food chain gives you the most small fries per order. • Problems: Daniel wanted to order onion rings, some fries fell out in the bag and became invalid, Wendy’s were confusing on their sizes, and all the fries were different sizes and lengths.

  4. Data – Wendy’s 5 Separate stops: • 18 • 23 • 24 • 26 • 25

  5. Data - McDonalds 5 Separate Stops: • 45 • 52 • 54 • 52 • 54

  6. Data – Burger King 5 Separate Stops: • 32 • 25 • 30 • 32 • 34

  7. Data Recap Table

  8. Inference Testing • Randomness: Random Sample of Fries Taken • Normality: - No Outliers but there is skewness so proceed with caution. • Equal Standard Deviation: W : 3.11 M : 3.71 BK : 3.44 3.71/3.11 = 1.19 < 2. Thus, the largest standard is not greater than the smallest standard deviation doubled thus standard deviations are roughly equal. W M B Mean number of Fries per order Wendy’s : 23.2 McDonalds : 51.4 Burger King : 30.6

  9. Calculations

  10. Conclusion • Since our p-value of .00000005657 is less than our alpha-level of .01 we will reject the null hypothesis. Thus, we have strong evidence that the true mean number of fries per small order at McDonalds, Burger King, and Wendy’s are not equal. • From carrying out this experiment, we learned that McDonalds, Burger King, and Wendy’s all give their customers an incredibly different number of fries per small order. However, each fast food restaurant gives fries of different sizes and quality, so we did not take that into account. If looking for sheer number of fries though, we would definitely go to McDonalds.

  11. Type I &Type II Errors • Type I: We say that each restaurant gives a different number of fries when they actually give the same. • Type II: We say that all restaurants give the same number of fries when they actually give different amounts. • A Type I error is worse because we want to be getting the most number of fries per order, so we don’t want to be going somewhere that gives less fries. • We will lower our alpha-level to 1% to reduce the possibility of a Type I error.

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