phase ii of coke analysis

8/2/2019 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

phase ii of coke analysis

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