Skittles Project

Michael Cullimore
Math 1040
Skittles Project Part 2
Confidence Interval Estimates
- Confidence Interval: A confidence interval is an indicator of a measurement's precision. It is also an indicator of how stable an estimate is, which is the measure of how close a measurement will be to the original estimate if an experiment is repeated.

The calculations show that we are 99% confident that the true proportion of yellow candies falls between 0.20125 and 0.21275. This is about one-fifth of the candies which does seem quite reasonable since there are five different colors in the bag of skittles. We are 95% confident that the true mean of candies per bag falls between 58.9481 and 61.0119. Using this information, we
can interpret that there are about 60 skittles in a bag, with plus or minus 2 skittles in a bag.

Hypothesis Tests
- Hypothesis Test: A hypothesis test is a way to test a claim that has been made about a population which could be made about the mean, proportion, or any other property of the population. Claims are tested against a selected significance level which can either be rejected or not rejected. If the claim has equality, then the hypothesis test determines if there is enough evidence to have a rejection of a claim. If the claim does not have equality, then the test governs if there is sufficient evidence to support the claim.

Our hypothesis tests for the bags of skittles tested the claims that 20% of all skittles are red and that the mean number of candies per bag is 55.
The calculations determined that in both cases the claims are rejected. In the case of the claim that 20% of skittles are red, the class proportion of 20.4% red skittles and is found to be unlikely to be correct and therefore is rejected because the calculated p-value is less than the significance level. Also, the claim that the mean number of skittles per bag is 55 is tested against the class mean of 59.98. This is also determined to be unlikely correct and is rejected as well because the calculated test statistic falls within the critical
value.
Hypothesis Testing Reflection The condition for a hypothesis test for population proportions is that np ≥ 5 and nq ≥ 5. In our case, np = (2579) * (0.2) = 518.8 ≥ 5 and nq = (2579) * (1-.2) = 2063.2 ≥ 5 so our samples meet these conditions and the test should be correct although the sample may not be the simple random variety, which disqualifies the result. The condition for a hypothesis test for the population mean is that the population is normally distributed or n > 30. In our case, the number of bags is 38. We can also determine if there is a normal distribution. In the graph below, we can see the frequency distribution and it is not very normal, therefore out samples do not meet the requirements for hypothesis testing and out test result may be wrong. We don’t have a strict normal distribution, which is what a standard deviation requires.
There could have been a few errors made using the data because our sample mean of skittles per bag might not be representative of the population mean. We can improve the sampling method by including many more samples, meaning more bags of skittles, and selecting those bags from randomized locations. Project Part 3 Reflection
Through the skittles term project, I could better understand how statistics can be used in everyday life. I have a better understanding of how statistics can be used to make sense using real world data. This project helped me learn the entire process of statistics starting with collecting data to drawing conclusions and being able to present results. Through this project, I was also taught that even though certain parameters may be small that an individual is testing, they must never make assumptions. A small bag of skittles provides results that I had never considered before. Through the project, I could see how my bag of skittles varied from others. This is one example of how a small sample can be very misleading and misinterpreted for a larger population. This lesson is something that I had never thought about before, but will be more conscious of it from this point forward. I used to not think much about math in my everyday life, and didn’t really think about how statistics influences me.
However, due to this project and stats class, the way I think about math has changed. Statistics is very different from the math I have grown up learning, and it felt more real and applicable to me. Statistics is something I can use in my everyday life, and I am better able to see where these applications can take place. The skittle’s project really helped convince me that math is used to make sense of all kinds of things, whether it be a math problem, different clinical trials, or food. This class has taught me skills that will be useful in both future math classes, content specific classes, and life in general. A few skills I have been able to gain through this project and course would include ways to organize information, how to make sense of all different kinds of raw data, how to present ideas and results, and how to apply statistics in any
situation. Through this project, I learned that a bag of skittles generally contains the same number of skittles in generally the same colors. While a few of the class results were different, much of results really surprised me. I always assumed bags of candy were filled at random, but I no longer think that way. The evidence collected from this project shows that candy companies do a great job of keeping things uniform and consistent (using a small standard deviation relative to the average, of course), although outliers can always occur. Statistics has helped me to understand that things aren’t perfect, and nor should we expect them to be. Before completing this project, I had no idea how to compile and use this type of data to help come up with the conclusions I did. Statistics has turned out to be very helpful and useful to me and is something I will be excited about using in my future.