Confidence interval of difference of means | Probability and Statistics | Khan Academy

Confidence Interval of Difference of Means

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[megan]

Wish I could like this video twice! You are single handedly getting me through my Biostats module in my masters. Thank you!!!!

[mattjelani]

This video helped a little but it's all over the place, definitely needs more organization.

[sammahdi]

Thought I'd just add a tidbit here since I find the terminology a bit confusing, and find some of the setup, especially the conclusion, unexplained or poorly explained (this results in some of the confusion in the comments). Anyone, please correct me if I'm wrong.

The intention of determining the confidence interval, is to see 1) Is there weight loss between the 2 diets and 2) How much? To that end, we need to determine, on average, what is the weight difference between the 2 groups (this is why you take the difference of the means). So now you have a new distribution, the distribution of the weight differences between group 1 and group 2. The next step, is to determine, within 95% confidence (i.e. 95% chance if I were to pick a random person between group 1 and group 2, they would have lost this amount of weight), how much weight is lost between group 1 and group 2. You do all the math, and you arrive with a confidence interval of 0.7 to 3.12lbs. This means if you were to pick 2 random people between group 1 and group 2, there is a 95% chance the weight lost between the 2 would be between 0.7lbs to 3.12lbs. Now to answer the 2 initial questions.

Is there weight loss between the 2 diets? Yes, because even the lowest value (0.7lbs) is above 0lbs. Again, this is not an absolute 100% there is weight loss (maybe if you do 99.9999% your range will be -1lbs to 5lbs, in which case there are people who haven't lost weight), but you are 95% confident (at least that's how I look at it). As to how much? Again, not an absolute 100%, but I am 95% confident with the data given, it is between 0.7-3.12lbs.

[sumedhakappagantula]

I owe Khan Academy 50% of my academic career

[opejojosephjedidiah]

All I can say may the good Lord bless more with wisdom 😊😊

[mikelcuvet]

Thank you for being the goat of explaining stuff my that my teachers cannot

[sijialiu]

The expected value of sample variance is an unbiased estimation of population variance, thats why the s is used to "replace" the σ of the population X1

[geraldh]

Thank you for helping me through Biostats.

[Ihatenicknames]

Thank you for the great video Sal! :D

I was thinking, maybe I am mistaken, but I don't believe that a 95% confidence interval means that there is a 95% chance that the confidence interval contains the population mean. Because if that was true, then, no matter how "far off" your sample mean was, there would always be a 95% chance that the confidence interval around it contains the population mean. This makes it seem as if the population mean is "moving around".

A 95% confidence interval means that 95% of all the SAMPLES you take, will contain the population mean. Not that one sample has a 95% chance of containing the population mean. 

[Faisal-wbnu]

I want to ask.. should the difference between two means be always postive? I mean X1 should be the bigger one so the result is positive

[dfsfklsj]

Hi khan, I think you might have a mistake here... You assumed the sample means are the true means of the population. Isn't it better if you can calculate a 95% confidence interval of the distribution of sample means of x1 and the control, and then say that the mean of their differences is 95%*95% between the differences of the calculated condifence intervals?

[luthojilimane]

Please include the formulas in your calculations

[nicolasscicolone]

Question, since the sample standard deviations of both samples were used (as opposed to population standard deviations) why was the z-distribution (and thus z-table) used to estimate the critical value for the confidence interval? Wouldn't a t-distribution and t-table be more appropriate? Thanks!

[LaBarness]

Thank you SO much for all of your video's Sal!!  They have helped me SO much!

[purplepandasrock]

its crazy how he talks so fast when he constantly stumbles over words and repeats himself and is always correcting himself. makes it hard to learn

[choppera]

I don't get the intuition behind why amalgamating the two sample means tells us anything?

[CCbean]

I love your video's, I t is annoying though that you repeat everything you say as soon as you say it.

[fraidym]

How come the true mean is x1-x2 and not x1+x2 divided by 2?? Thanks Sal for the video(s)

[DrAKMAnisurRahman]

Is it 1.96* sd or 1.96*SE (standard error?)

[sujeongmoon]

dont we need to calculate pooled variance?