Statistics 101: Single Sample Hypothesis Z-test Examples
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- เผยแพร่เมื่อ 26 ส.ค. 2024
- Statistics 101: Single Sample Hypothesis z-test - Part 2
Part 1: Conceptual Background
Part 2: Example Problems
Part 3: The Alpha Effect and p-values
In Part 2 of this video, we walk through two example problems involving single sample hypothesis tests including graphical representations of the hypothesis distribution. 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 how our selection of alpha (significance level) influences our rejection/nonrejection regions and Type I and Type II errors. Enjoy!
My playlist table of contents, Video Companion Guide PDF documents, and file downloads can be found on my website: www.bcfoltz.com
in 3:45, it should be Z < -1.96
Hi Eduardo! Thank you. :) Since the Starbucks example is a one-tailed test the critical value is 2.33. A z-score of 2.58 would be for the two-tailed test. Take care! - B
Thanks Lisa! I appreciate that so very much. However I think it is people like yourself that are out there learning who will save us all! :) All the best, B.
Annotated the missed negative sign per Arash NSB around 3:02. I said it correctly but missed the (-) on the slide. Thanks!
+Brandon Foltz if u are talking abt global recession in the above example, then how is that the salary wud increase. It will either remain the same or decrease. So, I feel it shud be one tailed ? what are ur views?
+Brandon Foltz how are u deciding alpha becos in first example u took different than the second one [starbucks] , please explain. Is it dependent on us ? What are the repercussions if we decide on our own and what are the repariations if it comes out wrong or their is some method to decide the alpha? thanx in advance. Once again , I want to reteriate that ur lecture are awesoem! keep it coming.
You are very welcome Rich. Thank you for taking the time to learn! - B
had seen other videos of hypothesis testing but your vdos are step by step and teaches what need to be done in what manner .
Thank you !!
Excellent video which is slow and therefore gives me time to take breaks in-between. I like the gradual progression of the videos. Thanks!
Hello! Critical z-values are found based on 1) the chosen level of confidence and 2) if the problem is a one-tailed or two-tailed test. In the front or back of every statistics textbook and on-line of course, you can find critical z-score tables. This video is for "z" scores (population) but you will also find them for "t" scores (samples less than n=100). Be sure to use the correct one for the type of problem you are working.
Brandon, first of all, thank you so much for these videos. I am taking statistics online, so I don't have the option withing my classroom to actually watch problems being solved. In this video in the Starbucks example, you have an alpha of .01 (99%), which has a critical z-value of 2.575 (according to my tables). In my tables, alpha of .02 (98%) gives the 2.33 critical value you used in the video. I just want to be sure I am not missing something in setting up the rejection region. This is the part of hypothesis testing I am having the most issues with. Thanks!
+Sandee Niles What you are talking about is the case of two tail hypothesis . In one tail hypothesis critical z-value is 2.33 at 99% confidence interval
Mr Brandon - tnx for all your videos, indeed.
Kristian Davidsen Thanks again. :)
Hi Prof. Foltz. Thanks again for all you do. I just wanted to ask a certain point of confusion for me. It was mentioned at 1:32 that the null hypothesis holds that the current and previous salaries are statistically the same, yet at 5:45 it stated that the null hypothesis (which we failed to reject due to the z-test score) holds that both salaries in question are statistically different. (?) Thanks.
HI Brandon, Theses are amazing, super-worthy classes. Way to explain complicated things. Thank you
Where does the 2.33 come from? I can't see where on the cumulative probabilities for the standard normal distribution table....:(
Hello, I have been wondering how to determine the z-score or z-critical value of alpha 0.5 percent, or 0.1 percent.
Is 72,180 sample mean already given?
its not give I think so
Yes
Hello Brandon, thank you for posting your videos! My question is how did you get the x̄ for the Business Analyst Salaries question?
Hello! The easiest answer possible, it is just a "given" in the problem. :) All the best! - B
***** For this question in particular the x̄ is not explicitly defined, so what would be my x̄ and why in this particular case?
Dr. Mary Story, an instructor in English Literature, suspects that 75% of her students prefer to write multiple-choice examinations rather than write essay examinations. To test her suspicion, she polled the 150 students in her class. Of the 150, 80 preferred to write a multiple-choice examination. Did this poll support her suspicions?
Hi
If you don't mind me answering, I'd say x(bar) is given from data. He didn't specify it on the question but should be given since the whole idea of doing z-test (or any other test) is to see how the value that I have from data (here, it's x(bar)) is different from what we've observed already ($69,873).
Very well explained, thank you for all uploaded videos
Isn't the z-critical value supposed to be 2.58 ??
Hey Brandon
Can you please explain a bit how you calculated the critical values and decision rule in step 4?
Great video, but I think you are missing the minus sign in z < -1,96 at --3:25--:-)
Hi! thanks so much for all your help. I have a question regarding the Starbucks example. Why did you take the null hypotheses to be that Starbucks is worse than though average? was it arbitrary? ( I always expect great service at Starbucks).
Thanks! Yes, the null can be somewhat arbitrary in many cases. Sometimes it is more clear cut like "There are in fact 16 ounces in this bottle of toilet bowl cleaner." or "Donald Trump's polling average is below 50%." It's a statement of assumption about the world.
@@BrandonFoltz got it. Thanks!
Is it ok to assume that Ho ≤ 3.25?
Hi Brandon! Thanks for your video. I find that if you let μ>3 to be the null hypothesis, it would be more likely to draw the conclusion that the average if greater than 3. So how do you usually establish the null hypothesis? I mean why in this case you choose μ3?
how to state the decision rule ? means in the second example of starbucks customer satisfaction question in step 4th we assume if Zalpha is > 2.33, we reject H0.
my question is how do we calculate or how the 2.33 value is come from?? please explain
Why are we using the hypothesized population mean in the z-test? Are we assuming that the hypothesized mean to be the current population mean?
Hi Brandon, thank you so much for these video. They are really great and makes learning easy.
My question is, in the second example ie the Star Bucks Satisfaction, how did you know that null is less than or equal to 3? it is not clearly mentioned what we are supposed to assume or claim.
Taking null greater than or equal to 3 and alternative as less than 3 would have worked too?
same question
please have an numercial example about anlysis of P value
The Starbuck case seems to be an example where the Type II error would be less harmful. So this alpha = 0,01 deos not sound as a good option.
I think you have it backwards. Remember that the null hypothesis is H0
this might be a really stupid question but what if the x bar is not given in the question? will we still be able to find it without the sample raw data??
RyTKu Hello! Never a stupid question. :) The mean will either need to be provided or calculated from data you are given or collect. In this case for the z-test, the sample would have to be large, at least n=100. Smaller and you would use the t-test. Hope that helps!
Thank you very much, great teaching
@3:35, in Step 4, should that be "z< -1.96"? I think so.
IDK if you'll read this or not but at 8:58 why have we established the hypothesis for null to be less than or equal to 3 I didn't get that.
Ikr me neither
Hi Brandon, I really appreciate your videos. I having a hard time though trying to input the values in my calculator. You don't have a population size. Can it be calculated with out the popN?
hey, thinks for your amazing videos they are the absolute best
in 9:00 why did you chose Ho to be less than or equal 3? to me it can be also Ho => 3.
what made you go with that null? I dont see any indication in question to go with ethier
Hi Brandon, I am a bit confused. When you made a video about confidence interval, you said that we could use the statistical tables to find the critical value, now you give us this formula for this z-value. I must have misunderstood something. I hope you can help me out.
Warm greetings
Maybe I understoood: the z critical value is the one we find with the table while the z value from our sample we find with the formula and based on the decision rule we draw our conclusions. At this point my question changes: the thing of point estimate plus or minus margin of error, is just not needed here? Or where is the connection?
+Brandon Foltz, how do you calculate the area of the rejection region? The critical value? I don't quite understand
So we always take 1.96 as a value of Z-alpha if it is two tailed hypothesis???
Nada Alsebaie when Alpha is 0.05
thnx a bunch. your videos are extremely helpful
This video was awesome - thanks!
Brandon Foltz, whenever we "compare" the data from the given population (mean and st. dev.) to our new sample, does it matter that they're not exactly the same N? does it present any statistical problem to be comparing different samples?
I hope this is not construed as nit picky but you said "accept the alternative hypothesis" at 12:25. Would this not be reinforcing bad habits to say this in this manner? As you said before, every statement regarding a decision should be made from a null hypothesis standpoint. Thus, technically we can never accept an alternative hypothesis but just reject the null.
Good day Brandon, thanks for the information shared, this has helped me understand the basic concepts of the critical value etc. I have a question, after we minus xbar from u divided by s.d, did you forget to complete the calculations? the second part with square of 112. I got 0.016 as my final answer.
How would we find the z value for rejection. For instance with the Starbucks example you said if Z > 2.33 then reject, but what gave you the 2.33? Good video though, I am learning more here than with my text book.
Awesome steps!!
Hello Brandon! How do I find the critical value for a certain alpha? Do I just memorize that a .05 rejection rate two-tailed test is +/-1.96 on the distribution? Thank you, and keep up the amazing videos.
Thank you! Its really very useful.
I see! Thank you for clarifying!
how did you get the sample mean for the first problem ?? pls elaborate
It is a "given" in the problem, but the sample mean us just the sum divided by the number of observations. 😊
Welcome Brandon, the other comment on the Binomial Distribution occurs in 4:16.... Can you suggest some good videos on Chaos theory, am very much interested in that. :)
I don't understand where you are getting the sample mean in these videos.
How do you do the ones that say: less than, between, or greater than?
Hi Brandon, First of all many many thanks for your lessons.
My question in this video is that we can the sample size is 112. we put it into z statistic and find out the value of z. But the z value came into non rejection region. Then you told that its just one sample ut we actually took 112 isn't? Please reply me at your earliest.
Is part 1 of these videos anywhere?
In the starbucks Example, it was decided that it is a one-tail test. How do we decide if the test should be a single-tail or Two-tail test?
Based on the hypothesis sign its decided.
At 9.07, how are we assuming the null hypothesis, it's not clearly mentioned..Can I go with Ho: mu>=3?
Since mean rating decided to be 3.25 so H0 will be Mu
Great vid..still i feel the z value for alpha 0.01 should be 2.58...pls specify
@ Revolver Aage Here is playlist for all hypothesis testing videos, included this one, part one, part 3 and other ones th-cam.com/play/PLIeGtxpvyG-IZRHcZcOy12jp7ywuRbE7l.html
Can somebody please explain the step 4? PLEASE. Would really appreciate it.
From where did we get Xbar ?
hii... i like ur videos... what will be the p-value for z=1.75 (first problem). I found it to be 0.040 which is less then alpha=0.05, which means we should reject the null hypothesis. but u said we cannot reject it as z=1.75 is less then z=1.96. Pls explain..
I dont get the step 2 how am i going to get that?
Great.. Thanks
Hey Brandon! Huge fan!
Thanks for such an amazing content. I don't know whether i am right or but i think you should have written we fail to reject null hypothesis that the old and current salaries are statistical not different at 5:35 min
felt the same way
THANK YOU
THANK YOU
THANK YOU
how to find z critical value?
Thank you soooo much!!!!!!
very instrodutional video.
Hi Brandon, in 03:29 wont it be negative 1.96, i think its a small typo.... otherwise great video as always....thank you.
Hi Amit! yes that is correct. Sorry I missed my - key one that one. Thank you for pointing that out. All the best my friend, B.
How did you get 72,180 for x/sample mean in the business analyst question?
i checked previous comments and many asked , Mr Brandon replied to one of them that its already given >> so i think it should be given in the problem !
thanks man
u r welcome but im a girl :P
LOL! Sorry..my bad
its okaay ^_^
Where did you get the x bar $72180 from?
It is just a given value in the problem. Thanks for watching!
Oh okay, thanks so much!
Sir, I didn't understand step 4, state the decision rule. I mean how can we get 2.33? Reply is needed urgently. :)
since alpha is 1%, the non rejection region is 99%, so we can see the z-table and find the value of 0.99 in it...it will show 2.3 on the vertical and 0.03 on horizontal..see z table on 2nd page at home.ubalt.edu/ntsbarsh/Business-stat/StatistialTables.pdf
Thank you!
how sigma is taken as $13,985 and sample count as112?i need reply urgent i got exam 2mrw.....
Hello! They are just "givens" in problem, provided so you can learn / do the analysis.
May I know why you don't use a p value to arrive to your decisions?
Einette Arevalo Hello! I do show the p-value method as well. It may be in the t-test videos. I teach the critical value first since that is where the p-value comes from. They are two ways of coming to the same conclusion.
***** Thank you for responding! Your videos are really helpful conceptually. So to get the p-value I would just have to look it up in the z score table where it says 1.75 and I would get the probability of the null? And since it's a normal distribution we would get a p value greater than or .05 and fail to reject the null? [this is with regards to the business analyst salaries] :)
Could someone tell me how he got $72180 as the sample mean ?????
even i have the same doubt man
Mean customer satisfaction at starbucks is obtained by making fun of employees who misspell their names.
How can we get z=2.33? please let me know
go to z table.. since alpha is 0.01, 1- alpha (which is 0.01)= 0.99, 5th column, 2.3= 2.33.. got it?
Hiya!
As the CL is 99%, we want to look up that Ha falls within the 1% level. you'd have to look in the percentage points of the normal distribution table, and look up the value of P=1.0
Sasithren Nathan But what if you don't have to z-table at hand, like you're in a test or something, is there any other way to calculate it? Or no, it's a must to have the table to know the value? Thanks!
Wonder Wyn as far as I know in that case z table must be provided.
the only suggestion I would have is could you somehow label all the videos as to where you should start. I understand they are topic, video 1 then video 2. However, if you could label them from beginning of statistics and then number them accordingly that would be very helpful as I have no real idea which video supersedes what.
Hiya! Best place to start is on the playlist page: th-cam.com/users/bcfoltzplaylists Everything is labeled and in order. No Playlist 02 since it would deal with graphing. PL01, 03, 04, etc.
Thank you for responding to my question so quickly! I don't even get responses from my professors that quickly.
+Brandon Foltz if our H0 is of the form "mu = a" the we use the lower tailed test ? kindly tell me if this is the correct understanding.