YSU Students. STATS 3743 Dr. Huang-Hwa Andy Chang Term Project 2 May 2002

Transcription

1 YSU Students STATS 3743 Dr. Huang-Hwa Andy Chang Term Project May 00 Anthony Koulianos, Chemical Engineer Kyle Unger, Chemical Engineer Vasilia Vamvakis, Chemical Engineer I. Executive Summary It is common knowledge that adults need, on average, 8 hours of sleep. In fact, college students require more than 8 hours of sleep per night do college students get the minimum required sleep needed? In order to determine whether college students meet the standard, a random sample of 100 students on the YSU campus was taken, observed, and analyzed. A survey included 1 average sleep per night for each student as well as whether that student lives in a dorm. Through vigorous analysis of the data, these conclusions were made: 1 The average YSU student gets less than the minimum requirement for sleep each night. Dorm life does not affect average sleep time for students. II. Introduction Finals week is upcoming, and with it comes a loss of sleep for many students. Some students even pull all-nighters, completely losing out on a day or days of sleep to catch up with all the material covered throughout the semester. Some may see this tendency as a result of procrastination, but that is not always the case. Although, finals week may lead to more all-nighters, many students habitually lose sleep throughout the entire semester just to keep up with the extensive coursework, their jobs, and the many extra activities they may be involved in. Is this truly the case? Is there any proof that the majority of students do, in fact, loose out on precious hours of sleep? If so, what is the average sleep for college students? Is Dorm life a factor in this case? These questions will all be answered in the context of this paper through an observational study. The data will be analyzed using different techniques like a two independent sample t-test and confidence interval estimate along with the help of SPSS If you think you know the answer to one or all of these questions, maybe you are in for a small surprise! 1

2 III. Data Collection Techniques In order to get an accurate and representative sample of the entire student body at YSU, the survey was conducted on different locations on campus and also at different times. The following are examples of some of the questions asked on this survey. Gender: M/F Dorm Life: Y/N Greek Life: Y/N GPA: Average Sleep: (hours/night) Work: (hours/week) Credits: Some of the data from this survey were omitted in our analysis. As much information as possible was recorded in order to have more data to work with rather than finding later in our analysis that our data must be thrown out due to insufficient description. The survey that was conducted was pretty cut and dry. It included stratified sampling which doesn t leave much room for bias. The survey was also conducted person to person without the use of a survey questionnaire. This helped in collecting data, since many people are opposed to taking the time and filling something out themselves. Also, it is much harder to have cases of non-response bias for this specific case. There were many considerations for analyzing other factors in relation to sleep patterns, i.e. GPA verses average sleep, but it was decided that there may have been a response bias in the GPA data collection since the survey was conducted face to face. In other words, some students may have stated a higher GPA than in actuality because they were embarrassed, whereas if the survey was conducted on paper, this may not have been the case.

3 IV. Summary of Data Numeric Summary: Refer to the table listed below for a full account of statistical values that will eventually be used in analyzing our data. Table 1 Description of Entire Sample (No factors taken into account) Average Sleep (hours/night) Statistical Value (SPSS) Mean % Confidence Interval Lower Bound: Upper Bound: % Trimmed Mean 6.53 Median 6.50 Variance Standard Deviation 1.6 Minimum 3 Maximum 1 Range 9 Average Sleep (hours/night) Table Description of -Independent Sample Statistics (Dorm life taken into account) Statistical Values (SPSS) Dorm life-yes Dorm life-no Mean N Standard Deviation t-test for Equality of Means Mean difference % Confidence Interval Lower Bound Upper Bound df 9 Sig. (-tailed) 0.71 t

4 Visual Summary: Refer to the graphs located below in order to get a visual representation of the data. Things are often clearer with the use of visual aids. These graphs will also be used later in analysis of the data. 40 Graph 1 Sleep Patterns of YSU Students (1) histogram 30 0 Frequency Std. Dev = 1.6 Mean = 6.6 N = average sleep (hour/night) Graph Normality Plot of Average Sleep (1) Normal Q-Q Plot 3 1 Expected Normal Observed Value 4

5 Boxplot Graph 3 Boxplot of Average Sleep (1) N = 100 Average Sleep V. Analysis 1 In order to make any observations at all, one must first determine whether or not their data is plausible. Referring to Graph 1, it is obvious that the data set follows a normal distribution. The histogram resembles a bell-shaped curve. Another way to show normality is through the normality plot (Graph ). The majority of the observed values are linearly related, which is good. Notice, however, the few outliers which are slightly deviated from the linear relationship. Also, the mean of sleep for students on the YSU campus is 6.58 hours, which is, in fact, lower than the required minimum. The standard deviation is 1.6. The 95% Confidence Interval is / This means that we are 95% confident that the sample mean lies within this interval limit. Next, the boxplot (Graph 3) signifies many things. The median is directly centered in the box meaning that there is relatively not much skewdness towards any half of the data. The range is reasonable, yet there are quite a few outliers that fall outside of the whiskers of the boxplot. Within this data set, there are both mild and extreme outliers. Sometimes these outliers have a significant impact on important statistical values like the standard deviation. In this case, the 5% trimmed mean is 6.53, which is very close to our actual mean of The outliers seem to have a negligible impact on our statistical values. To compare the average sleep of dorm students verses students who live at home, we conducted a hypothesis test, more closely a two independent sample t-test. The decision to use this type of test was based these assumptions: 5

6 We have two independent random samples, from two normal population with unknown variances Both of our populations exceeded 30 for an independent sample size of 47 and were normally distributed. The first step in performing a t-test is stating hypotheses. Null hypothesis: H o : µ d =µ n [Students who live in the dorms and students who live at home get the same amount of sleep.] Alternative hypothesis: H a : µ d <µ n (left-sided test) [Students who live in the dorms get less sleep than students who live at home.] Through the use of SPSS and/or the equation that goes along with our testing technique, we computed the t-value. Refer to Table for more SPSS output. Since σ 1 = σ, t = (x 1 -x -D o )/((s 1 /n 1 )+(s /n )) 1/ Where D o =0 Z= In a 95% (1-α%) confidence interval estimate, our level of significance is (α)=0.05, which makes our t α (t.05 )= In a left-sided test, like the one we are using, if t < t α, then the H o must be rejected. In this specific situation (t) > (t α ). Therefore we must accept the null hypothesis. College students sleep is not affected by dorm life. A 95% confidence interval of / implies that we are 95% confident that the difference of the means of our two samples will lie within this range. VI. Conclusions Finally, with finals coming up, it is a given that students will lose out on sleep. However, many college students lose out on sleep regularly, which is not a healthy habit. Maybe our culture is too fast-pace and too demanding of its people. At any rate, this study was very interesting. Although is seemed as though this was a simple study with a simple answer, it is surprising to find that dorm life does not affect the average sleep a student gets per night. This was a good study with a plausible sample set that was capable of being analyzed and dissected within the context of the material we covered in STATS this semester. This sample set was good to study since we tried to omit any limitations or biases in obtaining it. 6

7 We hope you enjoyed our presentation as well as our study, and we hope that you gained as much valuable information as we did and don t forget to relax and catch up with your sleep, its important! 7