The Sampling Distribution of the Difference in Sample Means (X_1 bar - X_2 bar)

I discuss the characteristics of the sampling distribution of the difference in sample means (X_1 bar - X_2 bar). I then work through an example of a probability calculation that involves these concepts.
The values for male and female heights are based on information in the 2009-2011 Canadian Health Measures Survey.

[@jbstatistics]

At 5:56 I'm discussing the sampling distribution *of the sample mean*, which has a variance of sigma^2/n. At 5:02 I'm discussing the distribution of heights (which is the distribution of the height for a single person, not the distribution of the mean height of n people), and the variance of this distribution is sigma^2.
I discuss why the variance of the sample mean is sigma^2/n when the sampling distribution is first brought up (in my "sampling distributions" playlist).

[@tomroth9964]

Thanks for the clear explanation. Love your videos by the way, best ones on the internet I've found so far.

[@jbstatistics]

You're welcome, and thanks very much for the compliment!

[@farahariyanti]

THANK YOU FOR THE CLEAR EXPLANATION, EASY TO UNDERSTAND

[@Adam-gp3ij]

I would like to say thank you so much ! I really learnt a lot from you and you are the best teacher ever !we really appreciate that efforts

[@jbstatistics]

Thanks for the kind words!

[@shannarudovclark]

I'm new to teaching statistics and I find your videos to be a valuable supplement to the text book because you explain the reasoning behind the equations that are usually just given in 'rule book' style. thank you!

[@SoumilSahu]

Just wanted to say this: I really respect the fact that you're trying to improve as a teacher, that's a rare mindset. As a student who is often frustrated by teachers who don't seem to try, I really appreciate this, even though you're not my teacher.

[@shannarudovclark]

@@SoumilSahu it's always nice to hear kind feedback, so thank you :)

[@fahada1921]

Thank you, sir.
You are the best.

[@jbstatistics]

You are very welcome!

[@nazdash]

Thanks a lot for video. Very clean and useful.
What will change if I need to calculate the difference between two weighted means?

[@TechSci_]

Great video!

[@zaynumar0]

you are a blessing

[@jacob476]

Way more concise than khan academy. Thanks

[@jbstatistics]

Yes, I try to keep things tight around here!

[@yt-1161]

you have some great stuff. not only the content also the presentation and I also like that the background is black. I can watch hours long on my phone without draining much battery.

[@jbstatistics]

Thanks! Glad to be of help!

[@someshagl90]

Thanks for the videos. They are really awesome. I have a small question in this video, At 8:20 , we subtract the mean (14.7) which was anyway equal to X bar m - X bar F. Doesn't this make the numerator within P zero? I did not get this part

[@vaishakmuralidharan7605]

Hi, I know this is late and you might have already figured this out. 14.7 is the mean of the sampling distribution of X bar M - X bar F. You can think of the difference of the two sample means as another random variable, say Y, the outcome of which is unknown because the outcomes of the two sample means are also unknown. 14.7 is therefore the mean of this said random variable Y.

[@tomroth9964]

At 5:56, why do you divide the variance by the sample size? (in X_m ~ N(177.7 , 5.6/20). Why is this not done at 5:02?

[@Jdonovanford]

Is that also called the standard error? (for the sampling distribution of the sample mean)

[@jbstatistics]

Many sources call the standard deviation of the sampling distribution of a statistic the standard error. But in my videos and notes I use the term standard error to refer to the *estimated* standard deviation of the sampling distribution.

[@hayaansari6800]

Look at 3:40 r u sure there will be + sign between var x1 bar and var x2 bar?

[@sahiraazhar9745]

what if the question is between 3.4 &5.9? is it still the same we do like normal dist?

[@jbstatistics]

If we need to find the probability the difference in sample means lies between two values, then we would use the same approach (standardize both values and find the probability that a standard normal random variable Z lies between the standardized values).

[@user-vk1zw9qz2f]

thanks

[@richashrivastava3981]

Why are variance added and not substracted?

[@sanaiqbal6352]

Awesome

[@jbstatistics]

Thanks!

[@yashnagda9363]

Previously it was
Z = x bar - u0 / sigma/sqrt(n)
But here x bar and u0 is reverse ehy is that.