Coke Analysis Phase II

8/2/2019 Coke Analysis Phase II

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Michael Trieu

Coke Analysis Phase II

April 22, 2012

Statistics 1510

Professor Brian Jean


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Abstract:

This experiment involves discovering and collecting data of the weights of each soda

can that includes Coke Zero, Diet Coke, and Diet Pepsi. The goal is to figure out which

one of these soda beverages weighs the least. This has been done by weighing

random soda cans of each type and comparing the data. This research should give a

pin point view of which soda can weighs the least.

Introduction:

Coke Zero, Diet Coke, and Diet Pepsi are known to be "lighter" soda beverages. We

want to figure out which one of the sodas is the lightest. These diet sodas have less

carbs and ingredients than there regular type can, therefore they should be different

methods into making the drinks lighter.

Methods:

We experimented and took data from three different soda brands that included Coke

Zero, Diet Coke, and Diet Pepsi. The supplies were given by professor Brian Jean

which were the three types of sodas, a weigh machine, and iPads to collect our data.

We were split into groups to find the weight of random selected soda cans and then

compare the weight of them to each other. The cans were labeled with numbers 1-68

for each brand, then we used the app TC-Stats to generate 15 random numbers. We

use the 15 random numbers to select a can that we can weigh for our data. My group

took turns gathering cans and collecting data for the soda. Our group hypothesized that


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Diet Pepsi weighed the most because It was a different brand then the other two,

therefore it was made in a different process that might make it more heavy.

The table and graphs of the Coke Zero dats gives us very vital information. The weight

of all the Coke Zero cans is 5565.72 grams. The mean is about 371.05 which is the

average of all the Coke Zero weights together. The sample deviation of 1.76 shows

how spread out the data is. Therefore, on average the the difference between each can

is about 1.76 grams around the mean. This information is a way of checking how close

we were able to keep reproducing the same results, the larger the sample deviation

equals more room for variation in our results. The lowest or minimum weight for Coke

Zero is 368.51 grams. The 5 number summary for Coke Zero describes the set of

observations which are also the most important sample percentiles. The first quartile

which is the same as the 25th percentile (25% of the data below and 75% above) is

369.64 grams. The median or the center data which is the same as the 50th percentile

(50% of the data below and 50% above) is 370.34 grams. The third quartile or 75th


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percentile (75% of the data below and 25% above) is 372.76 grams. The largest value

(maximum) we received out of the 15 data samples we took for Diet Pepsi was 374.09

grams. The graphs and tables show us that the data appears uniform.

The sum of all the Diet Coke cans came out to be 5589.79 grams. The average or

mean of the data is 372.65 grams. The 5 number summary for Diet Coke shows the

minimum at 369.61, first quartile at 371.52, median at 372.52, third quartile at 373.85,

and lastly the max at 375.85 grams. The standard deviation is about 1.66 which means

there was a little less spread than the Coke Zero standard deviation, therefore Diet

Coke was more consistent with its weights around the mean. The variance of the Diet

Coke data is 2.75. The Box and Whisker plot shows us that the data is mostly uniform,

but we can also say it is slightly skewed left.


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The collective data of the Diet Pepsi tells us the sum is 5536.79 grams. The mean is

369.12 which is the average of all the Diet Pepsi weights. The standard deviation of the

Diet Pepsi is 1.77. The variance is 3.13 which gives us information how spread out the

data on average. The minimum or lowest weight we recorded for Diet Pepsi is 365.54

grams. The maximum weight we recorded is 371.83 grams. The middle point in the

data came out to be 369.26 grams. The first quartile of the data is 368.26 and the third

quartile resulted in 370.92. The Box and Whisker plot shows that the data is mostly

skewed left shape for Diet Pepsi.

Confidence intervals show a close estimate of a sample or population, that indicates the

consistency of the estimate. 95% confidence intervals were done for each type of soda

beverage. Coke Zero's sample mean is 371.04 grams and has a standard deviation at

1.75 and a sample size of 15. The confidence interval shows that it's 95% confident

that true mean of Coke Zero weights fall between 370.07 and 372.02 grams. Diet

Coke's sample mean is 372.65 grams and has a standard deviation of 1.65 and a

sample size of 15. The confident interval suggests that it is 95% confident that the true

mean of Diet Coke weights fall between 371.73 and 373.57 grams. Diet Pepsi sample

mean is 369.11 grams and has a standard deviation of 1.77 and at 15. Lastly, the

confidence interval for Diet Pepsi shows its 95% confident that the true mean falls

between 368.13 and 370.10 grams.


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Coke Zero Normal Plot

Diet Coke Normal Plot


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Diet Pepsi

The normal plots demonstrate that Coke Zero and Diet Pepsi violate the assumptions

therefore they are not normal. If any of the sample groups violate the assumptions a

Kruskal-Wallis test must be performed. A Kruskal-Wallis is the non-parametric method

for trying to figure out if the samples originate from the same distribution. Also, with this

method it is based on ranks of the data. The median not the mean is used for this

method. The significance statements are that Ho: z= c= p and Ha: Not equal .


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The Kruskal-Wallis test tells us that the p value for the data is 6.096E-05 which is

greater than alpha (.05) therefore, we reject Ho because there is enough evidence to

show that at least one is different from another.

An ANOVA test would be used if all of the data was normal. It allows us to make

comparisons between independent groups. For example, if the data was normal the

significance statements would be Ho: 2/2=1 Ha: 2/2 does not equal 1. The

ANOVA test shows us that the p value is 8.378E-06 which is less that alpha (.05). We

reject Ho because at least one of the distributions are not equal.


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Results:


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The data comparison of all the weights of the soda cans gives us information, that we

can compare the weights side by side. The data tells us that Diet Coke had the highest

mean of 372.65 grams, concluding the average of Diet Coke was the heaviest of all the

three sodas. Also, the heaviest can at 375.38 grams belonged to Diet Coke. The soda

can with the smallest mean was Diet Pepsi, which also had the lightest can that was

weighed at 365.54 grams. Diet Coke was the most consistent with its weight because it

had the lowest standard deviation at 1.66 and a variance at 2.75. Coke Zero's average

weight resided in the middle between the other two soda cans.

Our groups hypothesis was incorrect because we believed that Diet Pepsi would be the

heaviest because it was manufactured in a different way than the two Coke sodas. The

result was that Diet Coke had the heaviest average of all the cans. The conclusion is

that Diet Coke is the heaviest soda can out of them three cans.


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Works cited

Jean, Meyers, and Rene Sporer. Data Analysis. United States of America:

3ringPublishing.com, 2004-2008.


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Appendix

DIET COK DIET COK DIET PEP DIET PEP COKE ZE COKE ZERResults Residuals

374.55 20 369.76 85 369.96 21 0 -0.8203

373.85 14 370.92 44 372.12 66 0 1.2409

371.52 48 366.17 61 368.51 64 0 -2.698

372.36 12 368.62 87 373.56 33 0 2.4707

373.22 9 371.08 34 368.71 11 0 -2.258

369.61 60 365.54 42 374.09 36 0 2.6127

370.38 43 367.82 32 370.07 23 0 -1.299

374.81 78 368.79 83 372.87 44 0 2.1264

372.52 29 369.53 18 369.45 69 0 -1.617

373.13 62 371.83 70 372.76 29 0 1.7794

373.71 44 368.6 96 370.31 17 0 -0.5888

372 56 368.26 30 369.64 2 0 -1.5

371.64 80 371.27 43 371.64 4 0 0.4491

371.11 55 369.34 12 371.69 5 0 0.4243

375.38 70 369.26 58 370.34 12 0 -0.3232


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Coke Analysis Phase II

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