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Mateo Solano

Stats 1510 Night Class

Diet Soda Can Weight Analysis

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Introduction

In order to ensure that the manufacturer is not losing money by over filling their

Product and at the same time not cheating their customers they must make sure that

Each product has relatively the same weight once filled. The same holds true for filled

cans of diet soda. Ideally the weights of any soda can should be relatively the same

weight once filled with liquid. The purpose of this research was to show that no one

brand of soda can when filled would on average weigh more or less than any other

brand of soda can. A simple random sample was taken of the following brands of soda:

diet coke, coke zero and diet Pepsi. Fifteen random numbers were generated using

tcsats so that each population was represented equally. Each brand of soda had

numbered cans where the population sample would be pulled from. The population of

each of the brands was the entire number of cans of each brand. For Diet Coke the

population was 85, for Diet Pepsi the population size was 96 and the population size for

Coke Zero was 72. Once these numbers were generated each numbered can was then

pulled from the population.

Methods and Materials

A simple random sample was taken of the following brands of soda:

diet coke, coke zero and diet Pepsi. In addition to the cans of soda the materials used

during this research a digital scale to weigh the cans and an Apple Ipad loaded with the

program TCStats. Each can that was used was specifically chosen

based on its assigned number which was randomly generated using the tcstats random

data feature. In order to accomplish this 15 rows were set and then the upper bound

number was set to 15 and the lower bound number was set to 1 and then the numbers

were generated beginning in row 1 and ending in row 15. Once the cans were pulled

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from the population each can was weighed on a digital scale and recorded in grams to

the nearest hundredth. The summary statistics were then generated for each of the

sample populations of soda cans. In addition to the summary statistics a Kruskal-

Wallis test was performed to verify if at least one of the weighted averages for the diet

soda samples was different from the rest.

Results

The summary statistics were as follows for each sample population of soda can

weights: Table 1.1 lists the five number summary for Coke Zero which was 368.28

grams for the minimum, 370.32 grams for Q1, 371.75 grams for the Mean, 373.27

grams for Q3 and 375.34 grams for the Max. For Diet Pepsi the five number summary

in Table 1.1 lists the figures as follows: 365.71 grams for the minimum, 367.26 for Q1,

369.26 for the Mean, 371.17 grams for Q3 and 373.78 grams for the Max. Finally Table

1.1 lists the five number summary for Diet Coke with the Minimum being 367.98 grams,

Q1 being 370.62 grams, 371.28 grams for the Mean, 373.94 grams for Q3, and 374.26

grams for the Max. The box and whisker plots for each of the diet soda samples are

graphed individually in Figure 1.1. You can see by the graphs that the Coke Zero and

Diet Pepsi have normal distributions but the graph shows that Diet coke does not have

a normal distribution. This abnormal distribution is shown by the normal plot graph

for the Diet Coke sample data. This graph is displayed as figure 2.1. Based on this plot

a Kruskal-Wallis test was performed which resulted in a p value equal to .0104 and so

Ho was rejected indicating that at least one of the diet soda sample means was different

from the other two.

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Table 1.1

Figure 1.1

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Figure 2.2 Diet Coke Normal Plot

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Appendix

Raw Data

diet

coke #

d. coke

weight D.Pepsi

D.Pepsi

Weight

C.

Zero

C. Zero

Weight1 370.89 15 368.69 6 372.143 371.21 21 369.13 10 3704 374.26 45 366.44 12 370.375 367.99 52 373.78 14 368.286 370.8 55 367.72 18 372.11

11 373.94 56 370.42 28 372.5215 368.83 60 371.17 33 373.6124 374 62 367.26 34 373.427 371.26 73 370.22 46 373.2739 371.09 74 371.64 48 375.3449 371.43 78 372.1 50 370.8153 370.8 80 366.81 56 369.9557 370.62 81 369.56 58 371.9964 367.98 89 368.25 68 370.3281 374.06 92 365.71 70 372.11