Finding a Correlation between Public School Lunch Meal Cost and Public School Physical Fitness Test in the State of CA

Overview

Objectives/Goals This experiment will determine if there is a correlation between public school lunch meal costs and the public school physical fitness test in the state of California. Methods/Materials After using a linear regression t-test to prove that there is a correlation I will then use the correlation formula to show a positive linear relationship between the two. If this relationship is seen, it will show schools with a lower lunch cost will have low percentage of students in the healthy fitness zone while schools with a higher lunch cost will have a higher percent rate of students in the healthy fitness zone. Data for county lunch costs and county fitness test results will be gathered from the California Department of Education website. Results The data supported my hypothesis. The linear-regression t-test showed that there is a positive linear relationship between the data. These results show that there is a correlation. Conclusions/Discussion Because my data comes from a census from all California counties and n is sufficiently large (satisfying the Central Limit Theorem), I was able to perform the t-test. I used my TI-84 calculator for the linear regression t-test. Based on the results from the linear regression t-test, I am able to reject the null hypothesis at the 5% level and even at the 1% level, therefore I accept the alternative hypothesis. This shows that there is a positive linear relationship between California county lunch prices and the percent of students in the Healthy Fitness Zone for that county. Based on the r2 value of 0.282, even with the alternative hypothesis accepted, the relationship is moderately weak with an r value of 0.53 and the linear regression line (y = 66.031 + 3.779x) only being 28.2% accurate. Because the data seems to be normally distributed along the residual plot, I can assume that the linear regression line is a good predictor for percent of students in the Healthy Fitness Zone based on a counties lunch price even with an r2 value of 0.282. With this statistical analysis I can conclude that there is a moderately weak linear relationship between county lunch cost and the percent of students in the healthy fitness zone. In addition the linear regression line can be used as a good predictor for the data.

Competition history

• CSEF 2015 Mammalian Biology · Entry S1210

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