Erin Powell

MAT 210

March, 18,2003

Does the amount of units a student takes, affect the amount of time that they have to work in a week?  By taking a convenience sample of forty Lake Tahoe Community College students, I expect that there is a correlation between the number of units a student is taking and the amount of hours they work in a week (r ¹ 0), causing the students with more units to work less than those students who are taking less units.  Therefore, the null hypothesis would state that there is no correlation (r = 0) between a student’s units at school and their hours at work.  I also expect that a student will spend more hours at work than they will at school.  Therefore, the null hypothesis states that the difference between the average hours a student works (m1) and the average units a student takes (m2) is equal to zero (m1-m2=0) and the alternative hypothesis is (m1-m2>0).

            Out of the forty students that were asked how many units they were taking, the mean is 11.0688, with a 5% trimmed mean of 10.9931.  With 95% confidence, I can say that the mean is within 9.6245 and 12.5130, with a standard deviation of 4.51599.  The minimum is 4 units and the maximum is 20 units, creating a total range of 16 units.  Although there is quite a large range between the minimum units and the maximum units, the median, as well as the mode (refer to graph #1 in back), is 12 units, which is the standard number of units for a full time student. 

            The average student in this sample works about 25.5750 hours with a 5% trimmed mean of 24.5278 hours and a standard deviation of 17.87835.  With such a large standard deviation, you can see that there is a very large range of hours that LTCC students work.  The minimum hours is zero, and the maximum is 70 hours, so the range is 70 hours.  Despite the large range, the median is 22 hours and the mode is 20 hours (refer to graph #2 in back), which both fall in the 95% confidence interval for the mean of 19.8572 to 31.2928 hours. 

            By examining the scatter plot diagram below, you can see that there is a low correlation between the amount of units a student is taking and the number of hours per week that they work.  With a correlation coefficient (r) of .060, very low correlation is confirmed.  Even though the least-squares line has a slightly negative slope (y = 28.199-.237x) creating a negative correlation and hinting that the more units a student takes the less they work, the p-value is .714 (or .357 for a 2-tailed test), which is way above a 5% significance level.  From this I can conclude that even with a larger sample, which tends to produce much more accurate results, the correlation between a student’s units and hours they work would still be low.  For this reason, I failed to reject the null hypothesis and determine that this data is statistically insignificant and conclude that there is not enough substantial evidence to say that there is a correlation between the amount of units a student is taking and the number of hours that they work.

Although there was no significant data to prove that there is a correlation between units and hours, a p-value of .000 for a 1-tailed test for paired differences (m1-m2) shows that the amount of hours a student spends at work is greater than the amount of units/hours that they spend in school.  The mean difference is 14.5063 with a standard deviation of 18.70027, and with 95% confidence I can say that the mean is between 8.5256 and 20.4869.  From this information I can say that this data is statistically significant and conclude that students do spend more time at work than at school and that I reject H   under a 1% significance level. 

            After surveying 20 males and 20 females, I can also conclude from this data that although females tend to take more units than males, males work more hours on average than do females.  With 95% confidence, the mean hours out of the 20 males surveyed, is between 20.2861 and 36.4139, and the mean hours worked out of the 20 females surveyed is between 14.1321 and 31.4679.  The median for females is 20, while the median for the males is 27.5.  With 95% confidence, the mean of the units for the 20 females is between 10.7150 and 14.5350 with the median being 13 units.  Again, with 95% confidence, the mean of the units for the 20 males is between 7.4138 and 11.6112 with the median being 8.75 units.

In conclusion of this survey, I have determined that my data is statistically insignificant to prove that there is a correlation between the amount of units that a student takes and the number of hours that they work in one week. I failed to reject the null hypothesis under a 5% significance level even though the graph suggests that there is a negative correlation.  To achieve more accurate results, I would need more money so that I could extend this survey with a much larger sample.  I would also need to do a stratified sample, rather than a convenience sample to represent more of a general population of students.  I would need to question day students, as well as night students, and question students from different schools.  The students at Lake Tahoe Community College do not represent the majority population of college students.  The second hypothesis stating that students spend more time at work than they do at school proved to be statistically significant and I was able to reject the null hypothesis under a 1% significance level.  As for the differences between males and females, although the data shows that males work more than females and females take more units than males do, the sample was too small to make a legitimate conclusion on the matter.  With more resources and more time, I could extend this survey and produce more accurate results on this matter.