Download - Phase II of Coke Analysis
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Soda Analysis: Coca Cola
Co vs. Pepsi Co.By: Alejandra Zepeda
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Abstract:
The experiment was conducted in attempt to obtaining information about the distribution of soda
liquid in 12oz soda cans. The motivation behind this experiment is to find out if the Coca Cola
Company or if the Pepsi Company did a fair job of filling their soda cans with 12oz. These
companies claim to sell 12oz cans of soda to the public. We collected data from Diet Pepsi, Diet
Coke, Coke Zero soda cans to conduct our experiment. Our experiment consisted of a population
sample of 15 soda cans from each population. The variable we measured was the weight of the
samples. The study consist of ratio scale data and a continuous variable. We did several tests and
assumptions to make sure our data gave us the best results. From our results we found out that
the Diet Pepsi Company was under filling their Diet Pepsi soda cans.
Introduction:
A problem emerged when several Diet Pepsi consumers complained about the filling of their
soda cans. Many of those consumers were opening Diet Pepsi cans that were half full. This
experiment was made to find out if this was true and to compare data with Coca Cola soda cans
too. The variable we measured is the weight of the cans in grams. In the experiment we will be
using new technology to find confidence intervals, distributions, and hypothesis tests. We
hypothesized that the Pepsi Company was under filling their soda cans and that the Coca Cola
Company does a better job at filling their cans with 12oz.
Methods:
The data was collected from populations of 96 Diet Pepsi cans, 72 Coke Zero cans, and 85 Diet
Coke cans. Each can was numbered from 1 to the total size of each population. The sample of 15
was obtained through randomization. It was used to reduce bias by implementing the simple
random sample technique. This technique is known to be reliable for giving an appropriate
randomized sample of a population. In fact, the simple random sample technique is best
indicated for this type of data collection because every possible sample of size n in the
population has equal probability of being chosen. The sample of 15 was obtained using an Apple
application called Tc-stats. This application was used to generate all the data analysis such as
summary statistics, hypothesis tests, histograms,normal plots, and t and f distributions. After the
samples were chosen we picked out the cans and weighted them. In this case, an electric scale
was used to measure the weight of each can in grams. We wrote down the weight in a data set
and saved it on Tc- stats. We kept the devices constant for each measurement. Consider that there
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is a chance of error due to the measurement process because the weight scale was not completely
stable at all times during the measurement of each can.
In Tc-stats we were able to identify if the distributions of each sample population are normal to
begin with. The normal plot for each population sample is in the appendix. The normal plot for
the Diet Coke is found in appendix A, Coke Zero is in appendix B, and Diet Pepsi's normal plot
is in appendix C. The data for Coke Zero showed to be normally distributed. The data of Diet
Coke and Diet Pepsi are not shown to be normal distributions because there are some data points
away from the line. Some of these outliers are making the population distribution heavy-tailed
and skewed to the left. With this information we are able to construct confidence intervals for
each sample. We did a one sample sign test for Diet Coke and Diet Pepsi because the
distributions violated the assumptions of a normal distribution. The significance level for all the
samples was .05. Then we proceeded with a Kruskal Wallis hypothesis test.
Results:
Below are inferences about each sample population. The total weight of the Diet Coke sample
averaged to 372.864 grams or 13.1523 ounces. There was a 1.334 standard deviation in the data's
variability(Fig. 1). Figure 2 is a pictorial representation of the data. The data for the Diet Coke
sample is skewed left (Fig. 2) so preferably we consider the statistic median, which is 373.19
grams or 13.1638 ounces.
Figure 1:
Figure 2:
Moving on to the second sample, the weight of Coke Zero had an averaged weight of 371.9173
grams or 13.119 ounces. It's variability is measured with a standard deviation of 1.9747 (Fig. 3).
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The distribution of the data seems to be mount shape (Fig. 4). Because of the shape of the
distribution the appropriate point estimate for data analysis is the mean.
Figure 3:
Figure 4:
The third sample is from the Diet Coke data. This sample data totaled to an average weight of
369.15 grams or 13.0213 ounces. From the mean, there was a 1.334 standard deviation
calculating it's variability (Fig, 5) The distribution is also skewed left like the Diet Pepsi data, so
the appropriate point estimate is the statistic median (Fig. 6).
Figure 5:
Figure 6:
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Based on the data we are 96.5% sure that the true median of Diet Coke is between 370.8237
grams and 373.0109 grams based on the sign test for median. We are 95% sure that the true
mean of Coke Zero is between 371.0900 grams and 374.8500 grams. Also, for Diet Pepsi we are
96.5% sure that the true median is between 367.7500 grams and 370.2900 grams also based on
the sign test. When we compare the statistical significance of these numbers we know that Diet
Pepsi's confidence intervals do not overlap with Coke Zero and Diet Coke. Therefore the
prevalence estimates are significantly different. In the other hand, Coke Zero and Diet Coke do
have overlapping confidence intervals. Therefore the prevalence are deemed to not be
significantly different. Based on the sign tests we can say that there is enough evidence to say
that the weight of Diet Pepsi cans weighted under 12oz. For Diet Coke and Coke Zero there is
insufficient evidence to say the cans are being under filled. To confirm this a Kruskal Wallis
hypothesis test says that there is at least one population sample that is different and by looking atthe data we can see that Diet Pepsi's data is the one.
Discussion:
We already know that Diet Pepsi, Diet Coke, and Coke Zero cans are labeled to weight 12oz. But
from our results we found that the Pepsi Company is under filling Diet Coke soda cans. This
means that some cans are not being filled at exactly 12oz but instead under 12oz. Our hypothesis
was right according to our results. We also understood that there was insufficient evidence to
suggest that the samples from the Coca Cola Company are under filling their Diet Coke andCoke Zero soda cans. We can assume that the Coca Cola Company and Pepsi Company are
filling each Diet Pepsi, Diet Coke, and Coke Zero 12oz more or less, but not exactly. The true
mean (12 ounces) that comes off the production line is really unknown. It may change each and
every time another can of Coke or Pepsi is filled.
Conclusion:
The 12oz label is really Coca Cola and Pepsi's hypothesized mean of the population. It is in
theory that the liquid inside the can measures exactly 12 ounces. This data is important because
we can find out if companies are being efficient. It is crucial for large companies like Coca Cola
and Pepsi to be wasting product by overfilling their cans or under filling. Because either way, if a
company over fills some cans then other cans are not being filled either. This data implies that
Pepsi Co is not being as efficient as it could be because some of their Diet Pepsi cans are being
under filled.
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Appendix:
Appendix A: Diet Coke Appendix B: Coke Zero
Appendix C: Diet Pepsi
The conversion of grams to ounces:grams 28.3495 = ounces
Kruskal Wallis hypothesis test:
null hypothesis: cz = dc = dp
alternative hypothesis: at least one is
(subscript cz is coke zero, dc is diet coke, and dp is
diet pepsi)
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Raw Data:
Bibliography:
Pictures for cover page were taken from:
Diet Cokehttp://www.freelogovector.com/key-diet_coke_clipart.html
Diet Pepsi
http://logos.wikia.com/wiki/Diet_Pepsi
Coke Zero
http://www.cokecce.co.uk/products/refreshments/coca-cola-zero.aspx
Weight/Diet Coke
Grams
Weight/Coke Zero Grams Weight/Diet Pepsi Grams
373.77 368.46 367.75
371.09 370.87 368.7
375.34 373.21 370.53
374.99 371.71 368.9
372.09 369.94 370.67
371.77 373.6 369.5
374.85 370.38 369.74
367.92 372.57 370.29
373.68 370.04 370.34
373.19 372.25 368.89
371.13 369.32 370.57
371.65 374.06 368.61
375.33 374.53 366.5
375.35 374.44 366.75
370.81 373.38 369.51