Statistics 101: Single Sample Hypothesis t-test Examples
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- เผยแพร่เมื่อ 27 ส.ค. 2024
- Statistics 101: Single Sample Hypothesis t-test - Part 2
Part 1: Conceptual Background
Part 2: Example Problems
In Part 2 of this video, we work on two real-world examples of single sample t-tests. We also discuss what happens when certain parameters in the test are changed. Finally, we examine how to find the exact p-value of the test.
For this type of test we are comparing a sample mean to a hypothesized population mean. We examine the rejection region, nonrejection region, and the critical values that separate them. Finally we learn to compute the t-statistic. Enjoy!
My playlist table of contents, Video Companion Guide PDF documents, and file downloads can be found on my website: www.bcfoltz.com
I salute you, mr. Foltz. In the dark ages of statistics I am finally seeing some light, thanks to your videos. Thank you very much!
I really can't believe all this content was free! The amount of hard work and dedication which you've put into this course is unmatched. You really are one of the best teachers here on youtube... Thanks a lot, Mr Foltz
This is the best, easiest to understand lecture I've seen on the internet. I am going to go back and watch the earlier lessons for my exams. Thank you also for the cheer-leading words of encouragement!
I never seen anyone would help us to learn and motivate us in the same time. that intro and ending motivate me so much. i'm subscribing!!
Thanks for the comment! I went back and listened again and from 23:20 to 23:25 I do say "cannot reject the null."
Watching this after 9 years of upload date. Still the best I could find on YT
Hiya! Right before that in Step 5, I give you the sample mean of $79,180. It's a "given" in the problem. We did not calculate it or anything. That is what we are comparing to the population mean.
I love how you include the positive, uplifting intros in all of your videos. It really does make me feel more motivated to watch your videos and study! :)
I CANNOT thank you enough for this. My stats prof has a heavy german accent and I can't understand a word she says. Youre a life saver!!!!
Oh you are very welcome! And yes, what I said in the video and and what you said in your comment are very close to the same thing. Basically, we just want to avoid saying we "accept" the alternative hypothesis. When we say they "are not the same" what we are saying statistically is that they likely come from different populations. In this case the populations would be "old salaries" and "new salaries." Let me know if I confused you more! ;) All the best, B.
Thanks for the video. This was a nice refresher without having to read through all the literature!!
***** You are very welcome!
Brandon, you are the best!! I am so grateful for your work and gifts to us.
Thanks for the prompt response. I was scratching my head on that one. Taking a psych tests/measurement class and its been about 3 yrs since I took stats so trying to review. I will be viewing you videos ALOT. Great instructing!
Seriously, you're doing a great job with these videos - they're clear, easy to understand, and application focused. Can't thank you enough - your explanations are easier to understand than my professor's lol!!!
Oh thank you Faraz! You just made my day! Best, B
I very much appreciate your going down to the conceptual level and explaining everything in a logical, coherent, and clear manner. Please keep these videos coming! Thank you!!!!
I think you just helped me save my grade for applied statistics :) *sniff* what would I have done without this video!?!?
I have been struggling with an online class and a cut/paste professor who doesn't explain things well. I am sharing your videos with my classmates so we can ALL pull out of this together! THANK YOU!
absolutely brilliant! SO clear, great examples and so so glad you even showed 2-tailed stuff, because everyone else shows one-tailed. Very very VERY good video thank you SO much!
Clear and humorous teaching!
I can't understand what the teacher said on Coursera about statistical inference. Then I came here and have understood the basic ideas of T-test. Thank you!
thank you a lot Professor Brandon, thank you for your help, I`m studying biostatistics subject at college, my major in Biotechnology. Your videos are great. Keep going Professor Brandon.
All love
Hello! Thank you for your comment. I went back and looked and I think that is what I said..."cannot reject the null hypothesis." Could you make sure for me? It is late and i am editing a video on ANOVA so my brain is a bit fried. Thanks! - B
Crystal clear examples! Thanks!
watched all videos, absolutely helpful. I now understand the concept of what i am actually doing. Thank you so very much.
Your videos have been so very helpful for me in understanding my statistics homework.
Thank you so much for these videos Brandon!
They have made everything so much clearer for me :)
Wonderful examples. Thanks Brandon..
Bravo bravo! Very impressed with your instruction. Your usage of the same example with modifications makes stuff even clearer. Your inspirational words at the start are worth it, dont need to remove them.
Well done Keep it up!!
Hi Brandon, Thanks for the helpful video's! A small tip to make these multiple part video's even better is to put links to the different parts in the description. This will make it easier to navigate to the beginning or end if you stumble upon one of the middel parts when browsing youtube.
Thanks again and keep up the good work! I think a lot of people will appriciate it.
thank you I got it. from previously commented on for someone's house. now I got it it's given in the problem. thankyou again I like the way you teach us.
Super lecture Videos Mr Foltz.. Thank you so much. You are making sense of all the complexities in Statistical world, through simple approach..
Excellent Presentation Sir..very Simple Steps to understand the matter
my brain is having a breeze, thank you Brandon
Hello! Thanks for the message. I made it up :) It is just a "given" part of the problem.
23:41 I think it should say since the area above t-statistic is greater than 0.01, we don't reject null
You're always so encouraging :-) :-). That's sooo nice! Few people go out of their way to express something that has true meaning like that. I so appreciate it...
Great and easy to follow!
Excellent video and explanation!
these are the best stat videos on the internet! Even better than the mighty Kahn's, IMO
That is very kind of you my friend. Sal is a hero of mine and to be mentioned in the same sentence is an honor. Without him what I do would not be possible. Thanks again and never stop learning! - B
Brandon GOAT over Sal.
I salute you for the good work done. These videos are very easy to understand. It's a great support to all beginners. Thanks a lot and best of luck to continue it further
Your work is superb. I appreciate your work and sharing your presentations. Thanks again.
Really a Great Teacher . I Salute you
very clear and well organized, great great work. Thank you so much
Excellent lecture series! I thought I was a good teacher, but once I saw yours, I have learned a lot.
Just curious, are the lecture slides available to download?
Excellent presentation. Thank you so much. You are really great teacher
thank you so much sir..you really made statistics easy..great work.
100/100 5 star explanation
could you please advise me the best books that i must read and understand to take my statistics to the highest level. if any coursera or any course is useful, i am happy to go through it too. please advise
Thank you so much for your detailed lecture
I have the same confusion. Did you find any answer?
hello! Thank you so much for your videos! They are incredibly helpful and encouraging.
Slight correction at 18:09, you said the t-value when the df is 24 and alpha is .01 would be 2.492, but it would actually have been 2.797. I think you may have looked into column .02 instead of .01 by mistake.
I'm new at this of course so I could be wrong, let me know if this is the case! Thanks again for taking the time to make these videos. :)
Thank you so much for the videos! Very helpful for me to understand the crazy stats!
Wow, thanks man, this really helped a lot!!! Thanks man!!
I'll ace that exam tomorrow :D. Thanks Brandon
It's a very useful video.I like the way of your presentation!!
Thank you so much Brandon - these are fantastic!
Your videos are a huge help...thanks!!!
thanks Mr. Foltz!! U made me love statistics, I always hated it.
Thank you Zahira! Loving statistics was always there, you just had to find it. Keep learning. Keep looking. You belong here. You got this. 🤘🙏👍
where did you get the sample mean 79,180 from?
It was the result of "gathering data" and calculating the mean from that. Of course he didn't really go out and gather data since this is just an example.
Really appreciate your help! This really helps me a lot👍🏻
very informative, thanks!
Excellent Explanation...Thank you!
awesome ! Enjoyed every second of the video. made my day !
This is very helpful. Thank you. Wish I seen this sooner.
keep going, nice, easy to understand
I think ginainberk is correct.
It should have been "Since these are greater than alpha, we can not reject H0" in the slide.
Awesome! very useful video. Many thanks for sharing.
I don´t understand what standard deviation means. For example here you state that s = $14,985 does that mean; the difference between the extreme high income to the lowest extreme income is $14,985?
Thanks for a great video!!! Really helped me a lot!!!
I cant grasp one thing, When we use t-distribution we assume that hypothesized mean is equal to the population mean and we also assume that 95% of sample means fall within certain area from hypothesized mean. But how can we be certain that this sample mean doesnt fall under Type 2 error? The 95% confidence interval just happened to catch this sample mean but we dont really know whether other sample means will be in this interval because they might belong to a different population.
Brandon, U are simply awesome !!!
You say that you "infer" the sample standard deviation of $14, 985, but you don't explain how you actually get the number. Can you clear up how this is calculated? Other than this, the video is EXTREMELY helpful, so thank you so much!
Hi Haley! It is just a "given" in the problem. Unless it is actually calculated as part of the video, it is a given. Thanks and you are very welcome! - B
The video really helped me a lot. Thank you!
Thanks Brandon for the wonderful videos. please explain how did you calculate the sample mean (x-bar) in example 1 of this video.
Hello! It is a "given" in the problem, but the sample mean is easy to calculate when needed.
Thanks for the video. I hope to know why the t table doesn`t consider the standard deviation? Look forward to your answer.
This saved me. Thank you so much!
Great video thanks for the explanation.
@23:30 ... you have a typo in your slide. you say verbally we can't reject the null, but you slide says we would reject the null
For the P Value of .043 and level of significance you say in words that we can not reject the null but in words on the slide it says we would. this can be confusing to others. but thanks for the videos!
Thanks Kyle! I added an annotation right there to clear things up. Best, B.
Thank you so much! Your videos are incredibly helpfull!!!
What I am missing is that if the new average is $79,180 and the old one was $69,873, it would seem that the current salaries are clearly much higher. I'm not clear on why this procedure would be necessary...or did I miss something?
But great video as always...
great video which is highly helpful
Thank you so much.I do have one question though. With your first example, your explanation was "Since the test statistic is outside the nonrejection region and beyond the critical value, we reject the null hypothesis that the old and current salaries came from the same population". I am confused by this statement.My question is could you also say that "we have sufficient evidence to reject the null hypothesis that the old and current salaries are the same" Is this correct?
Hey, you are one of the best teacher I have ever seen! Thank you very much about these videos! I have a question - for sample mean = 79 180, m = 69 873, n=12 and s = 14 985, I calculated that Test Statistic is 0,1793, but you calculated that it is 2.15 (10:38 ). Could you please tell me what I'm missing? I use this formula : (X_bar - m) / (s/sqrt(n)): 79 180 - 69 873/ 14 986 * sqrt(12). Thank in advance! I wish you all the best! Your videos are the great base for data science and data analytics!!!
Hi Elena, did you divide 14,985 by 3.464 (sqrt 12) first? Doing this would have given you $4,325.92. If you divide this number by 9,307, the outcome is 2.15
@@rehvajones8601 Thank you for your answer! My mistake was instead оf: 14 985 / sqrt(12), I was doing: 14 985 * sqrt(12). Yes, I have already received the Test statistic of 2.15. :) I wish you all the best!
Excellent! Best of luck to you as well.
very good and useful video
Hi, why don't you adjust the SD due to small sample size to SD+ = (n/n-1)*SD ?
Good stuff Brandon. Keep it up!
alhamdulillah...Allah bagi faham..
In the Starbucks example, it is noted that the mean rating determined to be 3.50 and the S is 1.4. Would you please explain how can we calculate the mean and standard deviation of likert scale response?
@23:24 since it is 0.043 i.e. greater than alpha.. you say we cannot reject the null hypothesis, but the slide says we reject the hypothesis..
Thank you very much sir
$791,80 just popped out of nowhere at 8:17. :)
How do you determine sample size when population mean isn’t given ( either conceptually or formulaically). This series is more about test statistics but this is post hoc for me. For example I did a baseline study for my job but I didn’t know how to determine sample size, and how could I if there was no population mean let alone sample mean to go off of if I was the one establishing such a study. I never got a straight answer even from PhD level folk. I’m aware of the 30 is when Gaussian starts to form but it seems not good enough, anti climatic answer. If I’m wrong on any of these points I concede, at this point I just need help. Your input Brandon or. Commenters would be greatly appreciated. Thanks.
This video would have been more instructive if you had included an example that showed how inappropriately using the normal distribution for a small sample size could impact the outcome of the test. That seems to me as the main pitfall. Otherwise, great videos! I've watched dozens of them. :)
Great stuff Professor Foltz. Rookie question here......the very first example, how did you determine the standard deviation to be 14,985? Thx..
How did you find the $79,180???
(btw thank you the videos!)
Hello Flavia! It is just a "given" in the problem like you would find in a textbook. It's just built into the problem.
Thank you man, I have Masters in Mathematics and I never understood inferential statistics until now! For those of you who got confused with how he got the 79,180. This was the initial sample mean salary of the Business Analysts provided from previous video. I think the confusion comes in from the fact that this mean was calculated from sample size of 12, and it is logical to say the sample mean of sample size would be different, particular in this case should be higher since choosing sample size of 15 falls on the right of the critical value. Therefore it came from another sampling distribution. The conclusion is the same and actually choosing the same sample mean help me understand your conclusion of that sample size has effect of either rejecting or accepting the Ho. Tell me if I am wrong, as you said earlier, increasing the sample size would increase the chance that the sample mean would be more closer to its true population mean, but I see there is chance that two sample sizes can have the same sample mean. So I see why you choose to have the same mean for two different sample size but in theory the n=15 should be closer to the mean by the Central Limit theorem. Thank you again, you the man.
16:34 - should not the null hypothesis be mean = 3.5 (remains the same) and alternate hypothesis be mean satisfcation level is 3.5 (i.e it can be either lesser or greater than 3.5)? making it a two tailed t-test?
Conceptual question here, Brandon. Given the likert scale is a categorical variable on an ordinal scale, i've always learned that taking the mean is pretty shoddy practice. Does a hypothesis test such as this one provide any meaningful results given this presumption?
Very good question! The answer is it depends. A lot of survey software treats Likert items as quantitative such as Qualtrics for example. Even though technically, as you said it is discrete, in practice those types of scales are treated both ways.
@@BrandonFoltz I don't know what is more impressive: the fact that you create such quality videos or that you care so much about our learning process that you respond to our questions (especially 10 mins after i comment!!). I sincerely wish you the best in the world. You've earned a subscriber and a fan for life.
where did you get the sample mean? I don't understand how? X bar =$79,180. when I calculate I get $79,394 am I wrong?
Which greater than or less than do I pay attention to ? The H0 is less than or equal to 3 and the H1 is greater than 3. I see from the video to follow the H1 to the right so it s a right tail but what s the point. I am guessing it is because we are testing the H1?
if you could please explain where you got df = t>2.201 thank you
Hey ***** I'm not understanding how you got .698 when you said multiply both sides. which variables do you multiply ? Help D:
Hi Brandon, Thank you sharing video, Good Examples, Just need to updae you. In this Video at Time Interval 23:20, Video Content does not match with your Voiceover on P-Value.
If P-Value is greater than Alpha Value we "FAIL TO REJECT NULL HYOPTHESIS", However video statement states "Since these value is greater than Alpha Value, We Would Reject Null Hypothesis"
I was confused, but i am clear after clealy listining your voice.