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Using TI calculator for P-value from t statistic | AP Statistics | Khan Academy

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    - [Instructor] Miriam was
    testing her null hypothesis
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    that the population mean of some data set
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    is equal to 18 versus her
    alternative hypothesis
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    is that the mean is less than 18
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    with a sample of seven observations.
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    Her test statistic, I
    can never say that right,
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    was t is equal to negative 1.9.
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    Assume that the conditions
    for inference were met.
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    What is the approximate p
    value for Miriam's test?
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    So, pause this video and see if you
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    can figure this out on your own.
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    Alright, what I always like
    to remind ourselves what's
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    going on here before I go ahead
    and calculate the p value.
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    There's some data set,
    some population here
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    and the null hypothesis is
    that the true mean is 18,
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    the alternative is that it's less than 18.
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    To test that null hypothesis,
    Miriam takes a sample,
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    sample size is equal to seven.
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    From that, she would
    calculate her sample mean
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    and her sample standard deviation,
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    and from that, she would
    calculate this t statistic.
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    The way she would do that or if they
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    didn't tell us ahead
    of time what that was.
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    We would say the t statistic
    is equal to her sample mean,
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    minus the assumed mean
    from the null hypothesis,
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    that's what we have over here, divided by
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    and this is a mouthful, our approximation
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    of the standard error of the mean.
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    The way we get that approximation,
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    we take our sample standard deviation
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    and divide it by the square
    root of our sample size.
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    Well, they've calculated
    this ahead of time for us.
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    This is equal to negative 1.9.
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    So, if we think about a t distribution,
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    I'll try to hand draw a rough
    t distribution really fast,
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    and if this is the mean
    of the t distribution,
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    what we are curious about,
    because our alternative
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    hypothesis is that the
    mean is less than 18.
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    What we care about is,
    what is the probability
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    of getting a t value that
    is more than 1.9 below
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    the mean so this right
    over here, negative 1.9.
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    It's this area, right there.
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    I'm gonna do this with a TI-84,
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    at least an emulator of a TI-84.
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    All we have to do is, we
    would go to 2nd distribution
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    and then I would use the t cumulative
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    distribution function so let's go there,
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    that's the number six
    right there, click enter.
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    My lower bound...
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    Yeah, I essentially wanted
    it to be negative infinity
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    and we can just call
    that negative infinity.
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    It's an approximation of negative
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    infinity, very, very low number.
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    Our upper bound would be
    negative 1.9, negative 1.9.
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    And then our degrees of freedom,
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    that's our sample size minus one.
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    Our sample size is seven so our
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    degrees of freedom would be six.
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    There we have it.
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    This would be, our p value
    would be approximately 0.053.
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    Our p value would be approximately 0.053.
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    Then what Miriam would do is,
    would compare this p value
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    to her preset significance
    level, to alpha.
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    If this is below alpha,
    then she would reject
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    her null hypothesis, which
    would suggest the alternative.
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    If this is above alpha, then she would
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    fail to reject her null hypothesis.
Title:
Using TI calculator for P-value from t statistic | AP Statistics | Khan Academy
Description:

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Video Language:
English
Team:
Khan Academy
Duration:
03:19

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