As an \"observational study\" (not an experiment) you decide to audit a session

ID: 3042123 • Letter: A

Question

As an "observational study" (not an experiment) you decide to audit a session of a current f2f Stat 200 class to see how it goes. You note that there is coffee available before the lecture begins and that fifteen (15) out of the 30 students in this class drink a cup. So, you decide to observe these two groups of students and note how long each of these coffee drinkers stays awake. (this is NOT a particularly random sample, hence the results are not that reliable, but they will be interesting). THIS IS ACTUALLY A KIND OF HYPOTHESIS TESTING WHICH WE WILL GET TO LATER IN THE COURSE. OUR (NULL) HYPOTHESIS IS THAT COFFEE DRINKING AND NON-COFFEE DRINKING HAVE THE SAME STAY-AWAKE TIME. OUR ALTERNATE HYPOTHESIS IS THAT COFFEE DRINKING AWAKE TIME IS GREATER THAN NON-COFFEE DRINKING AWAKE TIME. (THERE ARE BETTER STATISTICAL TEST AS YOU WILL COME TO SEE). BUT FOR NOT SEE HOW THIS WORKS OUT. Here are the times (in minutes) that each of these 15 coffee drinking students was able to stay awake: 33, 60, 45, 80, -5 (fell asleep before the lecture even started), 90, 100, 90, 115, 120, 80, 100, 90, 95, 100 Here are the times these 15 non-coffee (in class) drinking students stayed awake: 20, 50, 90, 120, 15, 30, 45, 60, 55, 45, 45, 60, 75, 80, 115 As an aside, after the lecture you decide that If you can stay awake for at least _____ (pick a number) of the 120 minutes the lecture lasts, you will get enough out of it to pass the course (this may be a bad criterion, but it’s the one you have decided to use). OK, now what statistical analysis do you perform on this data? Let’s go with CONFIDENCE INTERVALS. Explain why this is a good method and then CALCULATE a CONFIDENCE INTERVAL of your choice (75%, 90%, 95% etc.) for the time these 15 coffee drinkers' AND a confidence interval for the 15 non-coffee drinkers' awake time. Is the number of minutes you decided on being awake IN EITHER OF THESE CONFIDENCE INTERVAL? COMPARE THESE TWO CI's AND DESCRIBE WHAT YOU SEE AND WHAT YOU BELIEVE THEY TELL YOU ABOUT THE EFFECT OF COFFEE ON STAYING AWAKE (IN THIS CLASS)? DO YOU NEED COFFEE TO STAY AWAKE THE AMOUNT OF TIME YOU FELT NECESSARY? Bottom line: Is coffee the key to success in a f2f Stat 200 class? (Would it help in our on-line course?)

Explanation / Answer

Let X = the times coffee (in class) drinking students stayed awake

Y = the times non-coffee (in class) drinking students stayed awake

We assume: X ~ N(µ1, 12) and Y ~ N(µ2, 22)

100(1 - )% Confidence Interval for population mean is: {Xbar ± (s/n)(t/2)}, ….. (1)

where Xbar = sample mean, s = sample standard deviation, n = sample size and t/2 = upper (/2)% point of t-distribution with degrees of freedom = n – 1.

Using the above formula,

95% Confidence Interval for population mean 1 is: (61.03, 98.02) ……………………(2)

95% Confidence Interval for population mean 2 is: (43.15, 77.51) ……………………(3)

If at least 60 minutes of being awake in class is necessary to pass the exam, (2) above clearly shows that coffee drinkers stand a much better chance of passing the exam. ANSWER

Back-up Calculations

Group

Sample mean

Sample SD

Coffee Drinkers

79.53

33.39

Non-Coffee Drinkers

60.33

31.02