I am going to measure the circumference (in centimeters) and the seed content of 30 randomly selected lemons from the Montpelier Hunger Mountain Coop to determine if there is a relationship between the circumference of a lemon and the number of seeds inside of it. I expect to see a positive association between circumference size (explanatory variable) and seed content (response variable.) In an effort to ensure consistency, I will only use certified organic lemons from the same growing source, if practical. I expect the data to be fairly linear.

The experiment will be completed by selecting at random, at least 30 lemons, four at a time from the Hunger Mountain Coop. The date of the purchase of the lemons along with the measurement and seed count will be recorded in an excel spreadsheet for analysis once the experiment has been completed.

I will measure the circumference (the middle) of each lemon using the same measuring tape. Once the measurement has been made and recorded, the lemon will be cut in half along the circumference and the juice removed from each half using a hand held juicer. The seeds will then be separated from the pulp and counted. The number of seeds will then be recorded, making sure the seed count is accurately input next to the lemon that was measured. Only one lemon and seed count will be done at a time to ensure consistency and accuracy of both measures.

Once all of the lemons in the experiment have been measured and seed count input into the spreadsheet, the analysis phase of the project will begin.
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Test Subject

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Lemon Seed Experiment:

1) Based on the data collected, a well labeled scatter plot was created to show if a relationship between the two quantitative variables exists. My original assumption and what I expected to see what a positive linear association for circumference and seed count. Meaning, as the circumference increased the seed count would increase. As the reader can see by reviewing the scatter plot, there is no relation to circumference and seed count.
2) Correlation coefficient. I used technology to determine the correlation coefficient of -0.14261. This result further confirms there is no relation to circumference and seed count. My original assumption was that there would be a strong positive association. This assumption would have been supported if the correlation coefficient was 0.90 or higher.
3) Coefficient expressed as a percentage = -0.14261*-0.14261 = 2.03%
4) I was concerned there may be some lurking variable. Since I purchased the lemons from the same store, from the same producer and in a relatively short time frame, causes related to growing conditions or other environmental sources were mostly not a factor in the outcomes.
5) Least Square Regression: 16.78 + -.39. There is little to no value in this equation for this experiment as there is no strong positive or negative correlation to circumference and seed count.
Conclusion: As a result of the data collected and analyzed, using a sample size of 30 which large enough to make an assumption, it appears that, based on the data collected as part of this experiment, that there is no correlation between the circumference of a lemon and the number of seeds inside.
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