Statisitics AP project

Relationship between Observed and Advertised Measurement in a

500mL Great Value Purified Drinking Bottle of Water

Sergio Gomez-Avila and Alexandra Klay

AP Statistics

May 21, 2019

Introduction

Every day a person is predicted to consume between 2,700 and 3,700 mL of water.

Every year a person is predicted to consume between 985,500 and 1,350,500 mL of water.

Given these facts it is not an uncommon thing to say that water is important. In today’s society,

people do not always get what they are asking for rather they get less than advertised. We

decided to test a particular brand, Great Value Purified Drinking Water, to test whether or not we

are getting what we asked for. If we were to discover that we are actually getting less water per

bottle than what was advertised it would alter the amount a person drinks per day and overall per

year. We chose to do this study because water is such a vital part of our everyday lives, and if

we are getting less than we were told it would make no sense to continue to purchase this

particular brand of water.

Experimental Design

This study was conducted by selecting a random sample of a 40 water bottle pack of

Great Value Purified Drinking Water from Walmart. Out of the total 9 brands that are sold at

Walmart we conducted an SRS, 1-9, to choose which brand to conduct our study with. Then, we

did another SRS to select which case of 40 bottles of water of Great Value Purified Drinking

Water we would use by numbering the height, width, and depth, which came out to be a 5x5x5.

Once we had chosen our 40 pack of Great Value Purified Drinking Water we conducted our

study by using 2 500 mL graduated cylinders, 2 25 mL graduated cylinders, and 2 pipettes. The

purpose of the 2 25 mL graduated cylinders was to measure the excess water in a more accurate

manner than to use a graduated cylinder with a higher volume because it would lose accuracy

with the bigger diameter.

We computed a one sample t-interval with our hypothesis mean equalling the advertised

amount of volume, which is 500 mL. The reason we used a one sample t-interval was to

estimate an interval where the population mean of the amount of water in each bottle would

match the advertised amount. We also computed a t-test to see whether any differences we

found between the advertised and observed volumes of water were significant enough. The

conditions we needed to meet to perform these calculations were: attain a random sample, have a

sample that appears normal and if it was not, then the sample size must exceed 30, and each

individual observation must be independent and if it was not, the sample must not be more than

10% of the population. Since all of these conditions were met for the calculations, we had no

need to make any assumptions prior to our analysis. The null hypothesis is that the population

mean volume of the water is in fact what is advertised on the bottles and our alternative

hypothesis is that the population mean volume of water is less than what is advertised on the

water bottles.

Analysis

Pie Chart for Frequency of Rounded Measurements of Great Value Water Bottles

In our pie chart, the water measurement that had the most data values in their range was 515 mL.

Out of the 11 rounded whole number measurements, 3 values were similar at both 2% for 503

mL, 509 mL, and 510 mL, but also at 8% for 513 mL, 516 mL, and 519 mL. The two rounded

measurements that make up approximately 50% of our pie chart are 514 and 515 mL.

Box and Whiskers Plot for Rounded Measurements of Great Value Water Bottle

s

In the box plot above, the minimum data value was found at 502.81mL and the maximum data value was

518.99 mL. Our interquartile range, or IQR, was found to be 2.63 with our first quartile being 512.92 mL

and our third quartile being 515.55 mL. The median was found to be 514.465 mL.

Dot Plot for Rounded Measurements of Great Value Water Bottles

In our dotplot, the most common measurement when it has been rounded to the nearest whole

number is 515. Out of the 40 samples of Great Value Purified Drinking water, 10 samples were

found at 515.

Histogram for Rounded Measurements of Great Value Water Bottles

In our histogram there is a gap between 504 and 509 mL as well as between 511 and 512 mL.

The shape of our histogram is slightly skewed to the left with a range from approximately 503

mL to 520 mL. Our center can be found between 514 and 515 mL.

T-statistic Confidence Interval with 98% percent confidence and one-sided T-test

t-interval = x ± t * √n S x t =

√n S x x−μ o

● (average milliliters in sample)= 514.22975 ml x ● (standard deviation of sample)= 2.8893637730166 mlSx ● (t value for degrees of freedom of 39)= 2.42584 t * ● n (sample size)=40 Great Value Water Bottles ● (null hypothesis)= 500 ml μ o

The statistical significance with our one sample t-interval is that we can say with 98%

confidence that the true mean volume of Great Value Water bottles is between 513.122 and

515.338 mL. With a relative high margin of error due to our large confidence level, the lowest

measurement was still greater than 500 ml by 13.122 ml. Therefore, we can conclude there is a

98% probability the Great Value Water Bottles are over the advertised 500 Ll. We used a

one-sided t-test to investigate whether there is enough evidence to reject the null hypothesis of

the advertised 500ml Great Value Water Bottles and evidently, we calculated a large T-value of

31.1476 and a P-value of 3.63221 x 10 . As you can see on the T-Value DIstribution, it was −29

so large, it could not be displayed on the density curve and our p-value is undoubtedly smaller

than any significance level, which provides enough evidence to reject the null hypothesis that the

Great Value Water Bottles are truly 500ml but instead they are over by a significant amount of

water in milliliters. We cannot accept our Alternative hypothesis either because we were

expecting it to be lower than the 500ml when it was really over the advertised amount.

Limitations

One of the limitations we encountered was the fact that no matter how hard we tried to reduce

the amount of water that would inevitably cling to the sides of the graduated cylinders, pipettes,

and water bottle we could not extract the full amount of water into one place to get a complete

and exact measurement. Along with the limitation of water clinging to the sides of these

supplies, we also encountered the limitation of differently sized water bottles. Some bottles were

slightly indented on the bottoms or had a slightly thicker line in their design which are both

things that we could not change. We also had to round our data to nearest milliliter to present

better statistical plots and data because no one bottle was similar for when we measure to the

nearest hundredths of a milliliter.

Conclusion

We can conclude that with statistical applications that 98% of the time you drink a water bottle,

its volume will be greater than the advertised amount of 500 mL which means that for every 40

pack of water bottles you purchase from Great Value Purified Drinking Water, you will get one

free water bottle because even with the lowest mean amount of volume from the 98% confidence

interval of 513.122 mL, the sum of all 40 water bottles will be 20524.88 milliliters.

Duties

Sergio Gomez-Avila: conducted the observational study, created the graphs and charts on TI

nspire calculator, calculated the confidence interval, and formulated the conclusion

Alexandra Klay: conducted the observational study, described the graphs and charts, and wrote

data into context