AP Statistics Final Project

1. AP Statistics Final Project By Rachel Stark, Skylar Tupper, and Eleanor Konz Hour 5 Selvaag 2016

2. Is Dairy Queen all about their blizzards? Research Question: Is there a relationship between gender and purchasing a cone or a blizzard at Dairy Queen?

3. Why this topic? ~We wanted to know if there was a difference between the gender of people who order cones and the gender of people that order blizzards ~The most popular menu items are blizzards and cones ~We anticipated women ordering cones more than blizzards because women in general tend to watch what they eat and eat in smaller proportions. Of course there are always exceptions but this is overall what we expected. ~We hope to find no difference because we want women to not settle for cones and go big with a blizzard.

4. How did we collect our data? We did an observational study where we stayed outside of Dairy Queen on Sunday, May 15th between the hours 5:30-8:30pm observing the orders of customers. To make it as random as possible, we flipped a quarter (equally likely chance of heads and tails) to determine which customers orders we would record and which we wouldn’t. In our case, flipping a heads meant we would record the person’s order, and tails meant we would not. If we were recording a customer’s order, we would record their gender (male or female) and what they ordered (blizzard or cone.)

5. Graphs & Charts Raw Data

6. Graphs & Charts 36.2% of all blizzard customers are female 63.8% of all blizzard customers are male 36.4% of all cone customers are female 63.6% of all cone customers are male

7. Analysis in Context: What does our data mean in words? Of the 66 cone-buyers at Dairy Queen, 36.4% of them are female and 63.6% are male. Of the 105 blizzard-buyers at Dairy Queen, 36.2% of them are female and 63.8% are male.

8. Two Proportion Z-Test: Parameters and Hypothesis Parameters: Pb: The proportion of all blizzards orders from females Pc: The proportion of all cone orders from females Females were considered a success in our project Hypothesis: HO: pb-pc=0 There is no difference between the proportion of female blizzard customers to female cone customers Ha: Pb-Pc is not 0 There is a difference between the proportion of females blizzard customers to female cone customers

9. Two Proportion Z-Test: Conditions Conditions: Random: Data was observed and collected randomly with the use of a coin flip Normal: Approx. normal by LCC n1(p̂b) ≥ 10 and n1(1-p̂b) ≥ 10 105(.362) ≥ 10 and 105(1- .362) ≥ 10 38.01 ≥ 10 66.99 ≥ 10 There are at least ten females who order a blizzard and there are at least ten males who order a blizzard. n2(p̂c) ≥ 10 and n2(1-p̂c) ≥ 10 66(.364) ≥ 10 and 66(1-.364) ≥ 10 24.024 ≥ 10 41.976 ≥ 10 There are at least ten females who order a cone and there are at least ten males who order a cone. Independent: n1 is less than or equal to 1/10N and n2 is less than or equal to 1/10N 105 ≤ 1050 We know there are at least 1050 people who order a blizzard at Dairy Queen in Minneapolis (where the sample was taken) 66 ≤ 660 We know there are at least 660 people who order a cone at Dairy Queen in Minneapolis (where the sample was taken)

10. Two Proportion Z-Test: Name and Test Statistic Name: two proportion z-test Test Statistic: p̂c= count of successes in both samples combined success = female count of observations in both samples combined= p̂c= 62/171= .3626 Z= (.362-.364)-0 . z = -0.0264836982 √ .3626(1-.3626) + .3626(1-.3626) 105 66

11. Two Proportion Z-Test: Obtain P-value, Make decision, State conclusion Obtain P-value: p=0.984 Make decision: Because the p-value is not significant at the α=.05 level, or even as high as the α=.95 level, we fail to reject that there is no difference between the proportion of women who get a blizzard and the proportion of women who get a cone. State Conclusion: There is not strong evidence that there is a difference between the proportion of women who get blizzard and the proportion of women who get a cone.

12. One Proportion Z-Interval: Parameter & Assumptions P: The proportion of all people who go to dairy queen who purchase a blizzard Random: Data was observed and collected randomly with the use of a coin flip. Normal: LCC: 105≥10 66≥10 Independent: 10% condition→ 171≤1/10N → 1710≤N It is safe to assume that there are more than 1710 people who go to Dairy Queen and purchase a blizzard or a cone.

13. One Proportion Z-Interval: Name and Test Interval Name: One Proportion Z-Interval

14. One Proportion Z-Interval: Conclusion We are 95% confident that the interval from 55.14% - 68.66% captures the proportion of all people who go to dairy queen and purchase a blizzard.

15. Final Conclusion in Context Final Conclusion • There is not really a difference in the orders of men and women at Dairy Queen, meaning they are pretty much equally likely to order a blizzard or a cone regardless of gender. • When we took out gender as a factor, we performed a one-proportion Z-Interval and the results showed there was a difference in blizzard and cone purchases. This shows that customers are more likely to purchase a blizzard at Dairy Queen than they are a cone. Recommendations • I recommend asking the customers their gender and if the treat is for themselves or someone else. This will limit potentially false observations. • I also would recommend a different way to randomize which customers to record because flipping a coin was time consuming when there were a lot of customers Limitations/Error of Study • We had to assume people's genders • Time restraints • There are other types of desserts at Dairy Queen • We couldn’t tell if the purchaser was buying it for themselves or someone else • There are price differences between cones and blizzards

16. Peace Out!!