## Confidence Interval

You are trying to decide whether to take Stat 200 as an on-line or face-to-face class, but you don’t know if you can stay awake through an in-class, 2-hour (120- minute) lecture. It is critical that you are able to since the instructor has said that all of the quiz and final exam questions will come from material from those lectures. Recording them is ridiculous since who could listen to this stuff twice?!

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 HAS 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?)

FINALLY, what are some of the flaws in this observational study? How might it be better designed?

FOR REVIEWS Comment on what you have “confidence in” and say where you are unsure like the classmate you are reviewing.

**Solution Preview**

* Number picked is 80*

* I will perform t-test; t-test is the appropriate method to use since we want to measure the amount of difference about the change in our sample, and also most importantly the sample is less than 30 in either category.*

*(348 words)*