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The Chocolate Chip Conundrum

Mackenzie Kohler and Dorian Cheff
by

Dorian Cheff

on 16 May 2011

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Transcript of The Chocolate Chip Conundrum

THe CHoCoLaTe CHiP CoNuNDRuM Is there really 300 chocolate chips in each bag of Betty Crocker Chocolate chip cookie mix? By Dorian Cheff and Mackenzie Kohler We are interested in determining whether or not there are 300 chocolate chips in each bag of Betty Crocker’s Chocolate Chip cookie mix. To determine this, we will use a one sample t-test at α=.05. Afterwards we will perform a 95% confidence interval to determine the true mean number of chocolate chips in each bag of mix. HO: µ=300; The manufacturer’s claim is true and the average number of chocolate chips in each bag is 300.

HA: µ≠300; The manufacturer’s claim is not true and the average number of chocolate chips in each bag is either above or below 300. Conditions: Random: The mixed packets are going to be chosen randomly across the span of five days, five different stores, and six packets a day.

Normality: To ensure normality, we will have a sample size of n=30 bags of mix. Mechanics Conclusion What is the true mean number of chocolate chips in each bag of Betty Crocker Chocolate chip cookie mix? We randomly chose thirty bags of chocolate chip cookie mix; we chose six bags randomly from five different stores in the area. After collecting the samples, we counted the number of chocolate chips in each bag by sifting through the mix and picking out the chocolate chips. Our findings: Mean=323 chips, SD=18.979, n=30 Analysis Statistical significance vs. practical significance Scope of inference Statistically speaking, our sample, having a p-value of .0000003, is significant at the .05 level and signifies that the difference in mean is not due to random chance or a sampling error, allowing us to reject the null hypothesis. However, upon further investigation of the individual bags of chocolate chips, we discovered that the chocolate chips are actually smaller than the ones we are used to seeing in homemade cookies. We believe, then, that this difference in chocolate chip size does not increase the amount of chocolate in each cookie (there are more chocolate chips, but little change in the actual amount of chocolate), and therefore the increased mean number of chocolate chips is not practically significant. Because our samples were from local stores, our conclusions and findings can only be applied to bags of Betty crocker mis distributed to stores in this region. We reject the null hypothesis since p-value=. 00000028 < α at the .05 level. The evidence suggests that the average number of chocolate chips in each bag is not equal to 300. After conducting the confidence interval, we are 95% confident that the true mean number of chocolate chips in each bag of Betty Crocker’s chocolate chip cookie mix is between 315.91 and 330.09 chocolate chips. Because 300 is not in the interval, the evidence suggests that there are, on average, over 300 chocolate chips in each bag. Graphs Although we had a sample size of n=30, and assumed this would signify an approximately normal sample distribution, our graphs suggested that the data was skewed right. Upon questioning, we discovered that many manufacturers over-fill their bags. This, we assume, is to avoid any problems that may arise due to having under 300 chocolate chips in each bag.
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