Math 1040 Term Project

by Jayelle Hegewald, 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.

Variable 1: Average Hours of Sleep per Night

Variable 1 Hrs of Sleep per Night

Mean 6.6136365

Std. Dev 0.88996935

Min 5

Q1 6

Median 7

Q3 7

Max 8

Range 3

Mode 6, 7

Outliers None

Variable 2 GPA

Mean 3.4618182

Std. Dev. 0.33816618

Min 2.83

Q1 3.1

Median 3.59

Q3 3.65

Max 3.94

Range 1.11

Mode None

Outliers None

Variable 2: GPA

Results Simple linear regression results:

Dependent Variable: var2 - GPA

Independent Variable: var1 - Hours Sleep

Sample size: 11

r (correlation coefficient) = 0.2351585157

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.

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.

Results

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.

Contributions equally made by all group

members

Special thanks to our study participants!

Thank you