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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

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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

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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.

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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

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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.

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

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Data Number of Goldfish Trials

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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

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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.

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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.

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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.

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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.

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