1. IS THERE A SIGNIFICANT DIFFERENCE IN THE AMOUNT OF CLASSIC GOLDFISH IN A BAG THAN COLORED GOLDFISH? Madeleine Calvo & Allie Eckerman AP Stats period 7

2. Population of Interest The true mean amount of goldfish in a bag of “classic” goldfish The true mean amount if goldfish in a bag of colored goldfish

3. Randomization At Target, we numbered each package of goldfish and had our calculator randomly choose the 4 total boxes of goldfish that we bought. Next, we randomly chose the 15 pre-packaged bags of goldfish and counted out the number of crackers in each bag. We separated each bag we counted into separate piles to avoid miscounting.

4. Data Analysis Ho: M 1 = M 2 Ha: M 1 ≠ M 2 M 1 = Mean amount of classic goldfish in a bag M 2 = Mean amount of colored goldfish in a bag

5. Conditions Randomness Yes, we randomly chose the bas of goldfish off the shelf at the store. Independence Yes. (N>10n) (N>10(15)) (N>150). There are more than 150 bags of each type of goldfish in the population. Therefore, we can assume 10% condition was met for both samples. Normality Our sample size is less than 30, so we cannot use the Central Limit Theorem. Therefore, we must check graphs to determine normality.

6. Checking Normality Colored Goldfish Classic Goldfish The boxplots show no major skewness or outliers so safe to assume the sampling distributions are approximately normal.

7. Data Number of Goldfish Trials

8. 2 sample T-test Xbar 1 52.067 T-Value= 8.900 SD 1 =1.387 P-Value=1.852 x 10-9 n 1 =15 Xbar 2 46.933 df=26.605 (using calculator) SD 2 = 1.751 n 2 =15

9. Conclusion Since the p value is lower then any reasonable alpha level, we rejected the null hypothesis. Therefore, based on this test, we have reasonable evidence to prove that there is a difference in the true mean number of goldfish in a one ounce bag of classic goldfish vs. the true mean number of goldfish in a one ounce bag of colored goldfish.

10. Confidence Interval Since we rejected the alpha level we have to calculate a confidence interval to prove significance. (x ̄ 1 - x ̄ 2 ) ± t* (√S 1 2 /n 1 + S 2 2 /n 2 ) t* = 1.706 for a 90% Confidence Interval = (4.1504, 6.1163) We are 90% confident that the true mean difference between the amount of goldfish in a classic bag vs. the amount of goldfish in a colored bag is between 4.1504 and 6.1163 goldfish.

11. Confidence Interval Conclusion To further support our claim, we ran a 90% confidence interval. Since the test did not capture zero, the test proved significant difference between the amount of classic goldfish vs. colored goldfish in a one ounce bag.

12. SO… Based on our tests, there is significant evidence to prove that a one ounce bag of colored goldfish has less goldfish than a one ounce bag of classic goldfish.