The Professor's Response
In the video for example 135, you state that it doesn't really matter which we take as X1 or X2 (the weight watchers or the atkins). Well, I worked out the problem with you, having done the opposite calculation (you got -.9, I got .9 because I subtracted weight watchers from atkins instead of atkins from weight watchers).
The confidence interval I got had the same numbers but different signs:
Your confident interval in the video: [-3.85,1.78]
My confidence interval: [-.178, 3.85]
I worked everything else out with you in the same manner (t alpha/2, s2p, and E).
My question is if there should be a certain way that we evaluate these problems to determine which will be x bar #1 (X1) and which will be x bar #2 (X2). I don't want to calculate any which way and get the confidence interval wrong on the exam.
Here is example 135: Among 28 subjects using the Weight Watchers diet, the mean weight loss after a year was 3.0 pounds with a standard deviation of 4.9 pounds. Among 25 subjects using the Atkins diet, the mean weight loss after one year was 2.1 pounds with a standard deviation of 4.8 pounds. Construct a 95% confidence interval estimate of the difference between the mean weight losses for the two diets (assume weight loss is a normally distributed random variable). Does there appear to be a difference between the effectiveness of the two diets? Thank you for your help!
See the professor's answer below.
Hi Patti,
Good question. What I said in the video is correct. It doesn't matter which way you perform the subtraction. The way you did the problem is exactly correct, and that is why you got an equivalent answer to mine. **Assuming that you got [-1.78, 3.85] (you wrote something a little different above, but I assume that was a typo).
The interval is not just a pair of numbers, and if you treat it that way, you may miss some concept questions on the topic. The interval cannot be discussed without understanding the interpretation. It is this interpretation that matters, nothing else. For example, lets assume you used Weight Watchers (WW) as your first group. Then your interval would say that the true difference between WW and Atkins is between -1.78 and 3.85. Which says that there is not a significant difference between the two since the interval contains zero. The interval is more positive than negative, so it is also clear then that WW had the larger sample mean.
What is the interpretation for the other interval? [-3.85, 1.78] Since the subtraction was done Atkins - WW, we can say the following: The interval contains zero, so there is not a significant difference between the two average amounts of weight loss, and since the interval is more negative than positive it means the second sample mean was larger. The second sample mean is WW, so we have the exact same meaning for each of the intervals. We also have the exact same numerical differences (they differ in sign--as they should. After all 3 - 5 is not the same as 5 - 3, but the difference is 2 in absolute terms. The two results only differ in sign, which does not change the fact they they are different by 2 from each other.)
Again, there is no correct choice here, but you need to recognize an equivalent answer when you see one.
Sincerely,
Professor McGuckian
Watch this video for more on the topic: