Determining sample size based on confidence and margin of error | AP Statistics | Khan Academy

แชร์
ฝัง
  • เผยแพร่เมื่อ 6 ก.ย. 2024
  • Courses on Khan Academy are always 100% free. Start practicing-and saving your progress-now: www.khanacadem...
    Determining sample size based on confidence level and margin of error.
    View more lessons or practice this subject at www.khanacademy...
    AP Statistics on Khan Academy: Meet one of our writers for AP¨_ Statistics, Jeff. A former high school teacher for 10 years in Kalamazoo, Michigan, Jeff taught Algebra 1, Geometry, Algebra 2, Introductory Statistics, and AP¨_ Statistics. Today he's hard at work creating new exercises and articles for AP¨_ Statistics.
    Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help! Donate or volunteer today!
    Donate here: www.khanacadem...
    Volunteer here: www.khanacadem...

ความคิดเห็น • 55

  • @zhushuncai2642
    @zhushuncai2642 4 ปีที่แล้ว +32

    For people who don't know why p hat needs to be 0.5. The issue is we do not know the value of p hat before the researcher conducts the study. It could be 0.4, 0.3, or 0.01 based on the result. So if we want the margin of error to be no more than +-2%, we need to calculate the worst-case scenario in which p hat is 0.5. For reason I don't know, 0.5 * 0.5 is bigger than any other combination such as 0.4 * 0.6, 0.2 * 0.8, etc.
    Let's say we use 0.4 as p hat, and we get a sample size of 1537. We use this sample size and conduct the study, and we find out the p hat is 0.5. We do not have the sample size we need which is 2401 and the margin of error is more than +-2% which is not the result we want.

    • @qitang3813
      @qitang3813 3 ปีที่แล้ว +3

      The reason which you don't know may surprise you: A square has the largest rectangular area among all kinds of rectangles given a fixed circumference value.

    • @redpotter4074
      @redpotter4074 3 ปีที่แล้ว

      @@qitang3813 always interesting how arithmetic and geometry can come together

    • @qitang3813
      @qitang3813 3 ปีที่แล้ว +1

      @@redpotter4074 That's right my brother.

    • @thiagoazevedo9539
      @thiagoazevedo9539 3 ปีที่แล้ว

      The curve of the function f(p) = p(1-p) = -p²+p is a parabola, because it is a second-degree polynomial. A parabola always has a maximum or a minimum. In the case of p(1-p), its curve has a maximum, i.e., there is a value of p which yields the maximum possible value of f(p) = p(1-p). It happens that, in every parabola of a second-degree polynomial, the point of maximum or minimum is always in the average of the roots of the polynomial. Since the roots of p(1-p) are 1 and 0, the average value, which is the point of maximum, is 0.5! Everything I told becomes clearer if you study calculus, more specifically derivative. With calculus, you can better understand, among many other things, the process of finding the maximum or minimum of polynomials. Stay safe! God bless you. =)

    • @MrAdy0207
      @MrAdy0207 3 ปีที่แล้ว +2

      You can also compute the derrivative of -p^2 + p which is -2p + 1 and make it zero to get maximum resulting in p = 0.5

  • @FM-kz8vq
    @FM-kz8vq 4 ปีที่แล้ว +15

    I didn’t learn ANY of this in class & it’s on my stats test 🤦🏻‍♂️ thank you !!

  • @jgonz1325
    @jgonz1325 4 ปีที่แล้ว +21

    Why does this guy know everything

  • @wtenho1518
    @wtenho1518 6 ปีที่แล้ว +1

    Neat trick to calculate square numbers near 50: use (a + b)^2 = a^2 + 2ab + b^2, so (50 + b)^2 equals 2500 + 100b + b^2. In this case b = -1 => 49^2 = 2500 - 100 + 1 = 2401

  • @irakozenaftari4163
    @irakozenaftari4163 3 ปีที่แล้ว +3

    Thank you for great content but the formula could have been simplified to this n=(Z^2*p*q)/E^2 (1.96^2*0.5*0.5)/.02^2 = n=2401

    • @heyitsbbiii
      @heyitsbbiii 3 ปีที่แล้ว

      Does p hat 0.5 still be used even though I have a 99% level of confidence? Why or why not? I hope you could help me

    • @heleenpieloor8270
      @heleenpieloor8270 3 ปีที่แล้ว

      Wow, this makes it so much easier. Thank you

    • @irakozenaftari4163
      @irakozenaftari4163 3 ปีที่แล้ว

      @@heyitsbbiii Yes, if you don't know the value p, always use the .5 because that is where p hat is maximized.

  • @jonhadley8387
    @jonhadley8387 6 ปีที่แล้ว +3

    because we don't have P-Hat, just use N = 1 / ME^2
    pick the closest answer it will be off but close

  • @user-pu9il2jf3q
    @user-pu9il2jf3q ปีที่แล้ว

    Awesome explanation! THX!

  • @stitchedtogetherbunny
    @stitchedtogetherbunny 4 ปีที่แล้ว +9

    Why does p hat equal 0.5??

    • @rileylittle2421
      @rileylittle2421 4 ปีที่แล้ว +4

      The confidence interval is .95 ( I doubt you need this now though, sorry :c)

  • @noutalenezi8475
    @noutalenezi8475 2 ปีที่แล้ว

    Thank you so much this makes a lot more sense!!!!!

  • @MrArtbyart
    @MrArtbyart 3 ปีที่แล้ว +1

    I would expect that the sample size would vary with the population size. What if the total population is less than 2,000? Thanks

  • @bambino53
    @bambino53 4 ปีที่แล้ว +1

    Thanks my man you rule

  • @valdesito98
    @valdesito98 4 ปีที่แล้ว +1

    Hello, does anyonw know if there is a similar way to calculate stratified sample size? (without knowing the population size for each stratum)

  • @laurencooper9076
    @laurencooper9076 5 ปีที่แล้ว +16

    confusing introduction of p=0.5. why??

    • @sudiptasaha738
      @sudiptasaha738 4 ปีที่แล้ว +4

      p*(1-p) is maximum at p=0.5

    • @uniformstudy1294
      @uniformstudy1294 4 ปีที่แล้ว +1

      @@sudiptasaha738 if we take p = 0.5 then the sample which we will get will not be the smallest sample size.

    • @uniformstudy1294
      @uniformstudy1294 4 ปีที่แล้ว

      Please explain why we are taking 0.5 ?
      We require smallest sample size

  • @jaytums2818
    @jaytums2818 3 ปีที่แล้ว

    bruh ur a hero

  • @jeevanrana4076
    @jeevanrana4076 5 ปีที่แล้ว +2

    Can we take margin of error 2% when confidence interval 95%?

  • @noellecook3660
    @noellecook3660 4 ปีที่แล้ว

    Why does p hat have to be maximized? And why does .5 maximize it? Would using .5 apply to any margin of error percentage in which the p hat is unknown?

  • @SpittingBritTeaEarlGrey
    @SpittingBritTeaEarlGrey 6 ปีที่แล้ว

    Needed this

  • @jerome450
    @jerome450 6 ปีที่แล้ว +9

    Why did you use 0.5?

    • @TheRGuy
      @TheRGuy 6 ปีที่แล้ว +8

      You mean as large as possible.

    • @nastyhaterz
      @nastyhaterz 6 ปีที่แล้ว

      Because a normal distribution is assumed here

  • @zuhayranasrin7270
    @zuhayranasrin7270 4 ปีที่แล้ว +1

    you save meeeeee

  • @HoodSleepy2850
    @HoodSleepy2850 6 ปีที่แล้ว +1

    NICE FIRST

  • @drew75123
    @drew75123 6 ปีที่แล้ว

    Is this Cochrans formula?

  • @wildzach
    @wildzach 4 ปีที่แล้ว +1

    what

  • @fikilefm9221
    @fikilefm9221 2 ปีที่แล้ว

    how did get 2/196?

  • @junglecat4480
    @junglecat4480 6 ปีที่แล้ว

    Who made the formula? what is it called?

  • @joaovitorcampos6629
    @joaovitorcampos6629 6 ปีที่แล้ว +2

    what if my population is lesser than 2401??

    • @Gabrielabc42
      @Gabrielabc42 5 ปีที่แล้ว +1

      There's a different formula for a finite population

  • @adeyeyeoluwafemi8403
    @adeyeyeoluwafemi8403 4 ปีที่แล้ว

    please what is my samlpe size if my population is 3500

  • @lpsglitterpaws8536
    @lpsglitterpaws8536 4 ปีที่แล้ว +3

    very confusing!

  • @marianpalko2531
    @marianpalko2531 3 ปีที่แล้ว

    Might be a stupid question, but is this not at all affected by the total number of all of the community members?

  • @fallout6067
    @fallout6067 4 ปีที่แล้ว

    What if there's no margin of error available?

    • @chrispbacon3326
      @chrispbacon3326 4 ปีที่แล้ว

      Then you'd use z*(a/2) times StDev of the square root of n to get Margin of Error.

    • @chrispbacon3326
      @chrispbacon3326 4 ปีที่แล้ว

      StDev divided by the square root of n*

  • @callmecarpio
    @callmecarpio 5 ปีที่แล้ว +2

    Where did you get the 1.96?

    • @girleatsbread
      @girleatsbread 5 ปีที่แล้ว +1

      The t-table, if you look at the bottom, 95% confidence gives a z score of 1.96

    • @yashhooda293
      @yashhooda293 5 ปีที่แล้ว +1

      you can also use your calculator menu - 5 - 5 - 3 and then put area in as .025 and leave mean to 0 and standard deviation to 1 and you will get -1.95996 which is the same thing as 1.96 according to my AP Stats teacher, hope this helps :)

  • @pelasgeuspelasgeus4634
    @pelasgeuspelasgeus4634 10 หลายเดือนก่อน

    So, you found the sample without caring about the population size. Does it make sense to you? It sounds like pseudoscience to me.

  • @anthonycarbonaro7890
    @anthonycarbonaro7890 5 ปีที่แล้ว

    You made a total mess out of something very simple.
    n=(z alpha/2 * theta/E)squared.