Math 1040
Cavities vs Soda Consumption
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Written Project.pdf Size : 209.942 Kb Type : pdf |
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Smile pdf.pdf Size : 460.822 Kb Type : pdf |
Ryan Hermansen
Math 1040
Ruth Trygstad
Soda Consumption Vs Number of Cavities
Our first quantitative variable is daily soda consumption. The unit of measurement for this variable is ounces. Values for this first quantitative variable are 12oz, 24oz, and 36oz 48 oz.
Our second quantitative variable is how many cavities a person has had. The unit of measurement for this variable is one unit for every one cavity a person has had. Values for this second quantitative variable are 1 cavity, 2 cavities and 3 cavities 4 cavities
The research question is "Is soda consumption related to a person getting cavities?"
To answer this research question, the group will gather data as follows:
We would obtain 42 people for the random sample. To accomplish this we would use a systemic sampling process. The goal would be for each of us to collect seven responses, from the contacts in the mall/work. We would start at the 7th contact, and sample every 9th contact until our desired number of responses has been collected.
|
Group 12 Data |
Soda (oz) |
# of cavities |
|
Jessica |
336 |
0 |
|
|
168 |
10 |
|
|
0 |
0
|
|
|
336 |
20 |
|
|
32 |
3 |
|
|
24 |
3 |
|
|
112 |
40 |
|
Heather |
24 |
0 |
|
|
12 |
2 |
|
|
84 |
0 |
|
|
0 |
3 |
|
|
0 |
0 |
|
|
6 |
4 |
|
|
0 |
1 |
|
Ryan |
0 |
3 |
|
|
20 |
8 |
|
|
60 |
20 |
|
|
12 |
2 |
|
|
30 |
7 |
|
|
12 |
2 |
|
|
0 |
1 |
|
Ashlie |
12 |
20 |
|
|
12 |
4 |
|
|
20 |
1 |
|
|
0 |
0 |
|
|
84 |
24 |
|
|
0 |
3 |
|
|
24 |
4 |
|
Chris |
12 |
5 |
|
|
24 |
5 |
|
|
0 |
12 |
|
|
0 |
3 |
|
|
0 |
18 |
|
|
120 |
9 |
|
|
48 |
4
|
|
Column |
Mean |
Std. Dev. |
Median |
Range |
Min |
Max |
Q1 |
Q3 |
Mode |
Outlier |
|
Soda
|
46.4 |
82.524574 |
12 |
336 |
0 |
336 |
0 |
48
|
0 |
336, 168
|
R (correlation coefficient) = 0.2982
Equation for line or regression: y = 0.032x + 5.402
Difficulties/Surprises
There were not too many surprises or problems that we encountered while doing this project. I would say the hardest part, was getting the participants of the study to give accurate estimates of the amount of soda they drink. This variable had the most outliers, and made the scatter plot a little all over the place, as well as other visual representations of the data. Other than that, everything was very straightforward and easy to accomplish.
Analysis
Both of the variables were well distributed, we had a wide range of data in the samples we collected, which gave us a more accurate reading. There seemed not to be a close enough correlation in the data, the R value we collected, was less than the critical value from the table. Our critical value was 0.349, when using a 0.05 level of significance, and our R value was 0.2982 which meant that we had to reject our null hypothesis and accept our alternative hypothesis. All in all, this stated that there was in fact no relation between soda consumption and an increase in cavities over the lifetime of a given person.
Interpretation/Conclusion
Although our R value and the critical value turned out to have to correlation in one another, I think if the data had been more accurately dealt with, in the response from the participants, there would have been a change in the data which would have shown a relationship between these two variables. Possibly, cutting out some of the ‘extreme’ values in this project, then redoing the R values, would prove this point. But for the sake and integrity of the collecting and data itself, we need to read it and accept it at face value for what it is. I think we have answered the original question, by finding that, there is no correlation between soda consumption and the amount of cavities a person has had. Although it is not the answer we were looking to get, it is the answer which the data revealed.
Reflection
Our initial question was, does soda consumption have a direct relation to the amount of cavities acquired during one's lifetime. We concluded that there was no direct correlation between the two variables, for the data we collected. The R-Value came to 0.2982, which is reasonable, but no where near the amount needed to prove solid evidence. Our correlation coefficient was 0.05, with 33 degrees of freedom. Although, the evidence was not as convincing as we were hoping, we concluded that although soda consumption may not be a direct effect, it is at the very least a contributing factor. Luckily, we did not run into many problems during our experiments collecting the data. The only obstacle, if there had to be at least one, would have been the quality of the answers which we were recieving. Some were unsure of the amount of cavities they had in the past, and some were unsure of the amount of soda they took in, so a sampling error could have occurred along the way.
To sum things up, I believe the data we collected and analyzed gave us a good answer, that it is not an immediate problem, but something that can be, if allowed to be. . As the soda consumption went down the amount of cavities went down as well, and vice versa.. This shows a correlation in the data, not much, but some. So for us, it is important to take care of your teeth, and little things such as rinsing your mouth after drinking a soda, drinking the soda during a meal instead of the span of an entire day, and using a straw to prevent contact with our teeth, are just a few ways we can reduce the risks of getting cavities down the road. Our understanding of statistics grew immensely, espeically in the idea of just how hard it is to make sure you collect data that is random, and unbiased in any way shape and form. It shows us how important this is, and what to look our fot, when presented with statistics in the future.