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This project investigates whether there is a direct relationship between GPA and average hours of sleep per night for students in a statistics class. Utilizing a random sampling method, we selected 11 participants and performed a simple linear regression analysis. The correlation coefficient obtained was 0.235, indicating a weak relationship. Our findings suggest that while a relationship may exist, it is not statistically significant, and factors such as maturity level, work status, and interest in education might influence the results. A larger study could provide more insights.
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Math 1040 Term Project by JayelleHegewald, Michele Houtappels and Melinda Gray 2013
Introduction • Our group aimed to answer the question “Is GPA directly related to the average hours of sleep per night for students in our statistics class?” • In order to answer this question: • Method used: Random Sampling Method. • Each member of the class population was assigned a number. • The sample was obtained by using a random number generator. • 11 students were selected. • Members of the sample were contacted via email. • 4 students did not respond. • Another 4 were randomly chosen by the above method.
Results • Simple linear regression results: • Dependent Variable: var2 - GPA • Independent Variable: var1 - Hours Sleep • Sample size: 11 • r (correlation coefficient) = 0.2351585157
Results • Our sample would normally accurately reflect the population, as it was done by the random sample method. But, with such a small sample, the performance of a few individuals can have a large effect on the outcome. So, it would more accurately represent the population if the sample size were larger and the study repeated. • We may then find the data to be more normally distributed with a stronger correlation. As it stands now, one may infer that there is no relationship between average hours of sleep per night and GPA, but we have not ruled that out. A more accurate study could very well show a stronger relationship. • In analyzing our information, our correlation coefficient is 0.2351585157, which is fairly close to zero and indicates that there is little or no evidence of a linear relation between the two variables. • In comparison, a correlation coefficient at+1 is a perfect linear relationship and -1 is a perfect negative linear relationship. Therefore, there may be a relationship still, but not as strong. • Also, in comparison of our value “r”, correlation coefficient, and our sample size, it has been determined that there is not a statistically significant relationship between average hours of sleep and GPA, r(9){9 refers to degrees of freedom, sample size-2}=0.2351585157, p>0.05. P>0.05 meaning that our correlation coefficient “r”, 0.2351585157, was less than the critical value determined, 0.602, from the table. So we cannot be 95% confident that a relationship exists. • So, as far as correlation, there may still be a relationship between the two variables, but the correlation coefficient is letting us know that it is not a very strong relationship.
Conclusion • In conclusion, there is some evidence of a relation, but it is weak. This conclusion is supported by the correlation coefficient. • There could be “lurking” variables such as: • Maturity level of the student. • Work status (i.e. fulltime, part time) • Time spent on recreation. • Interest in education. • Amount of credit hours the student is taking. • The hours of sleep the specific individual needs in order to function properly.
Thank you • Contributions equally made by all group members • Special thanks to our study participants!
