Z Tests for One Mean: Introduction

An introduction to Z tests for a population mean mu. These tests are appropriate when sampling from a normally distributed population where sigma is known. I discuss the hypotheses and the underlying logic, and work through an example. I do not discuss the rejection region or p-value in an in-depth way in this video -- I discuss them in other videos, and provide links at the end of this one.

Пікірлер: 77

  • @kotanvich
    @kotanvich3 ай бұрын

    Finally I’ve found best source of statistic knowledge

  • @jbstatistics

    @jbstatistics

    3 ай бұрын

    I've always been here :)

  • @nickbeauregard3019
    @nickbeauregard30196 жыл бұрын

    These videos are the perfect complimentary study guides for my grad-level stats courses. Thank you so much. I wish my tuition dollars were going to you.

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    I'm glad to hear you find my videos helpful! I'm very glad I could help.

  • @alexmuffles7431
    @alexmuffles74318 жыл бұрын

    I have a test tomorrow; today, all these statistics are finally making some sense. Thank you!!!!!!

  • @cavallotkd
    @cavallotkd9 жыл бұрын

    You are awesome!!! thank you so much for these videos, they are crystal clear and make the study of statistic a real pleasure. THANK YOU!!!!

  • @jbstatistics

    @jbstatistics

    9 жыл бұрын

    You are very welcome Andrea! I'm glad to be of help.

  • @jingyiwang5113
    @jingyiwang51138 ай бұрын

    Thank you so much for your clear explanation! All your videos are of great help to my coming exams!

  • @aaryannakhat1842
    @aaryannakhat18424 жыл бұрын

    My goodness! I salute you.. You have made me fall in love with statistics!

  • @kathl3n341
    @kathl3n3415 жыл бұрын

    You are my blessing! Thank you so much!

  • @tchesarebordjia6180
    @tchesarebordjia61807 жыл бұрын

    Great Videos. Thanks for your work!

  • @linneajohansson3796
    @linneajohansson37963 жыл бұрын

    This was very well explained. Thank you!!

  • @M4zku
    @M4zku8 жыл бұрын

    Fantastic videos! Thank you.

  • @BoZhaoengineering
    @BoZhaoengineering4 жыл бұрын

    Your explanation is clear! Much much better than the confusing textbook. I found my textbook I read is terrible no one is going to understand it .

  • @marbiengregory5976
    @marbiengregory59768 жыл бұрын

    Very organized presentation! Thank you so much.

  • @jbstatistics

    @jbstatistics

    8 жыл бұрын

    +Ar Mar Bien Gregory You are very welcome!

  • @BahadirSimsekMD
    @BahadirSimsekMD8 жыл бұрын

    best video i've ever seen regarding this subject.

  • @rsadsultanov3071

    @rsadsultanov3071

    3 жыл бұрын

    So have I

  • @chengzongyang835
    @chengzongyang8353 жыл бұрын

    the best stats video regarding hypothesis testing on earth

  • @jbstatistics
    @jbstatistics11 жыл бұрын

    Comic sans is terrible. But Chalkboard, which is the font used in the annotations in this video, is well known to symbolize refinement and class. I question your visual acuity and perceptiveness.

  • @jbstatistics
    @jbstatistics11 жыл бұрын

    I used pnorm(-17) to get P(Z < -17) and then used the symmetry about 0 argument.

  • @NToB36
    @NToB366 жыл бұрын

    Many thanks for your clear and concise videos

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    You are very welcome!

  • @dontbesosick
    @dontbesosick7 жыл бұрын

    very high quality videos thank you

  • @basharc
    @basharcАй бұрын

    Your videos are easy to understand while being in-depth. The other videos I've come across are either overcomplicated or not comprehensive enough. How to know whether we should divide by sigma or sigma x bar when finding z-value?

  • @MrAlbashiri
    @MrAlbashiri8 жыл бұрын

    thank you for the videos. i have learned a lot from your videos.

  • @jbstatistics

    @jbstatistics

    8 жыл бұрын

    +Mohammed Al-Bashiri You are very welcome. I'm glad to be of help!

  • @abrahammathew8698
    @abrahammathew86983 жыл бұрын

    I went through multiple videos on hypothesis testing, but your videos are best. Thank you so much. Just one doubt, If after plotting QQ plot if we find sample is not normally distributed then what would be the go forward?

  • @Lexibugss
    @Lexibugss11 жыл бұрын

    Thank you!

  • @manjeetsingh-rc3gb
    @manjeetsingh-rc3gb5 жыл бұрын

    sir ji your i love ur teaching..

  • @hessamlatube
    @hessamlatube5 жыл бұрын

    Thank you for these awesome videos. I have some suggestions for the playlists and captions. 1) I think it would be a good idea to number the playlists, so that it would be easier to know which playlists should be covered first. 2) Some videos might need prior knowledge, which are already address in another video. Putting a reference to the prerequisites of such videos would be very helpful for people like me. I am watching your videos to pass a Random Variables course, and also as a prerequisite for Design of Experiments course. Thanks again.

  • @williamundall6988

    @williamundall6988

    5 жыл бұрын

    if you go to "playlists" on his channel all videos are numbered and put together in different topics

  • @jennmatwychuk709
    @jennmatwychuk7096 жыл бұрын

    AMAZING. THANK YOU.

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    You are very welcome!

  • @dontbesosick
    @dontbesosick7 жыл бұрын

    could you do something on time series analysis, i.e AR Models, White Noise

  • @pranoschalsaikia5024
    @pranoschalsaikia5024 Жыл бұрын

    Please explain me this: when you proved normality assumption by Q-Q plot, did you mean that the sample was taken from a population following a normal distribution or distribution of the sample means will follow normal distribution?

  • @Lexibugss
    @Lexibugss11 жыл бұрын

    What did you type in to R to get P(Z>17)=4.1x10(-65)?

  • @SashankAryal
    @SashankAryal7 жыл бұрын

    Where did you get the data to make boxplot and qqplot?

  • @johnnguyen3115
    @johnnguyen31159 жыл бұрын

    good! i like the words below videos

  • @sivasakthi76
    @sivasakthi763 жыл бұрын

    Could you please explain why the test statistic Z will have standard normal distribution when Null hypothesis is true? I'm not able to understand why it is so.

  • @gardenmenuuu
    @gardenmenuuu2 жыл бұрын

    Thank you sir!This video is 8 years old but well organized.I am curious which software did you use at that time.I dont know if you are reading this ,but if you are please reply 😁

  • @adityamathur2363
    @adityamathur23638 жыл бұрын

    thank you :)

  • @rishabhchopra6418
    @rishabhchopra64187 жыл бұрын

    Hey! I'm watching all of your videos linearly! Don't have many doubts till now, it's amazing :D One question: If we had known the probability of selecting a tuna piece which has more than 0.40 ppm mercury content. Then we can have a random variable X = # of tuna pieces with more than 0.40 mercury content and n = 16 X = {1,if mercury content is higher than 0.40 0, if mercury content is lower than or equal 0.40 } Then, could we have inferred something from the Binomial Distribution?

  • @rishabhchopra6418

    @rishabhchopra6418

    6 жыл бұрын

    you cannot make a binomial distribution here. You don't know the probability of getting a success or a failure, here.

  • @eceserin
    @eceserin Жыл бұрын

    I love you man! Here, I said it.

  • @playmakersmusic
    @playmakersmusic2 жыл бұрын

    Thank you so much! Even after 9 years, this video still provide so much value. May I ask, when you say that "If the null hypothesis is true, this value that we get here should simply be a random sample from the standard normal distribution", does it mean that should Z fall into the range that you showed in the boxplot diagram(of the 16 tuna), it would mean null hypothesis is true?

  • @jbstatistics

    @jbstatistics

    2 жыл бұрын

    No, it doesn't mean that. I don't mean to be a jerk, but it means just what I said --- if the null hypothesis is true (and the assumptions are true), the value of the Z test statistic will be random sample from the standard normal distribution. The standard normal distribution is a probability distribution. Under H_0, the value of Z that we get will be a random sample from this distribution.

  • @playmakersmusic

    @playmakersmusic

    2 жыл бұрын

    ​@@jbstatistics No you are not a jerk and I am really appreciative of the fact that you are helping people like me who have no statistics background. I was really confused about the random sample part, but I guess it was meant to be hypothesised right? Thank you!

  • @jbstatistics

    @jbstatistics

    2 жыл бұрын

    @@playmakersmusic It's a bit of an abstract concept and if you don't fully grasp it then it's not the end of the world. The major implication of that notion is that values of Z near the middle of the standard normal distribution are ordinary, everyday values to get from that distribution, so they don't provide any evidence against the null hypothesis. Values far our in the tails are unusual values to get from the standard normal distribution, so they provide evidence against it. That's oversimplified, but the gist of it.

  • @playmakersmusic

    @playmakersmusic

    2 жыл бұрын

    @@jbstatistics I get what you mean now! I was watching your other video where you used Pete as an example. It makes so much sense now! Thank you so much!

  • @rechrowm4276
    @rechrowm42766 жыл бұрын

    nice explanation I now can do my dam sw XD you're a life saver man

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    I'm glad to be of help!

  • @bilgeturkkan6095
    @bilgeturkkan60955 жыл бұрын

    Why is it the case that if H0 is true, the Z test statistic will have the standard normal distribution?

  • @andresescobar2814
    @andresescobar28146 жыл бұрын

    Is there a difference between hypothesis testing about a population mean and hypothesis testing about a population proportion?

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    That depends on what you mean by "difference". The basic notion is the same, and a binomial proportion is a special type of mean, but the two tests are not exactly the same.

  • @emptyxnes
    @emptyxnes10 жыл бұрын

    Do you have a video on the quantile-quantile?

  • @jbstatistics

    @jbstatistics

    10 жыл бұрын

    Only on the normal QQ plot, not QQ plots in general.

  • @calavino223
    @calavino2237 жыл бұрын

    how do i get p(more than or equal to 17) without using the software. help please.

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    You need to use software to find this value. One could, conceivably, approximate the integral numerically by hand, but that definitely wouldn't be practical.

  • @edwardraywer4198
    @edwardraywer41986 жыл бұрын

    Thanks...

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    You are very welcome!

  • @KieranMace
    @KieranMace8 жыл бұрын

    why not calculate sigma_x_bar (at 8:35) from the sample data?

  • @jbstatistics

    @jbstatistics

    8 жыл бұрын

    +Kieran Mace You can't calculate sigma_Xbar from sample data, as sigma is a numerical characteristic of the population. If sigma is unknown, then you can estimate it with the sample standard deviation s, and we do that when we carry out a t test. But if sigma is known, as it is in this video, then we would use it rather than an estimate of it.

  • @scgaming34
    @scgaming347 жыл бұрын

    I have a question, what if there is no x bar?

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    X bar is the sample mean. If the sample data hasn't been collected yet, then you can't carry out a test. (But you can map out what test you would like to carry out.)

  • @scgaming34

    @scgaming34

    7 жыл бұрын

    well, in the example given to me by my teacher, there is a mean, a standard deviation and sample size, but no x bar... and the problem involves computing the probability of a type one error

  • @hounamao7140
    @hounamao71407 жыл бұрын

    look at what you did, saturday morning and first thing I did is turn on my computer to watch statistics video, could it be.. oh god am I getting to like statistics ?!

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    There's much to like. Learning statistics is a great way to start the day!

  • @atmanx5
    @atmanx59 жыл бұрын

    Thanks for these videos, very helpful .1 question How come here Z=(XBAR - mu)/(sigma/sqrt(n)) but in the standardizing normal random variables video Z=(XBAR - mu)/(sigma). Can someone please clear this up for me.

  • @GuppyPal
    @GuppyPal2 ай бұрын

    Z score of 17... So you're telling me there's a chance. 😏

  • @jbstatistics

    @jbstatistics

    2 ай бұрын

    Always 😀

  • @kzterminator
    @kzterminator7 жыл бұрын

    Lost myself at quantile

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    Quantiles have that effect on people.

  • @kzterminator

    @kzterminator

    7 жыл бұрын

    What's a quantile quantile chart?

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    A quantile-quantile plot allows for a visual assessment of whether two sets of data come from the same distribution, or a single data set comes from a specific theoretical distribution. In my videos, I discuss the normal quantile-quantile plot. This type of plot allows us to visually assess whether the normality assumption appears to be reasonable.

  • @MDMAx
    @MDMAx2 жыл бұрын

    4:07 H0 isn't true. Hos ain't loyal.

  • @PantsMenace
    @PantsMenace11 жыл бұрын

    comic sans! nooooooooooooooooo