WEBVTT
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all right, were given some data about graduates and
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there salaries 10 years after graduation, and we've divided
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them into data for men and data from women.
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So for part A, given the statistics Ah,
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we're given a sample of 40 men, and we
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want to find the probability that our sample mean will
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be within 10,000 of our population. Means hold on
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. Gonna crack that notation. There we go on
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that might need his penmanship, but you get the
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general idea, right? So let's find our standard
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deviation of the sampling distribution. It's gonna be the
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standard deviation over sample size. So that's gonna be
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, uh, 40,000 divided by the square root of
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40. That equals 6324 56 We're gonna find a
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Z lower and see upper like so. So for
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a C lower, uh, it's gonna be negative
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. 10,000 divided by our center deviation, uh,
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for the sample. Yeah, our sampling distribution,
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and then for upper, it's gonna be 10,000 positive
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. When you compute these out, you get negative
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1.58 from 1.58 Comparing this to our normal probabilities table
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. This gives you probability. Lower 0.571 probability,
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upper 0.9429 Uh, this means our probability is gonna
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be probability upper minus probability, lower. Which is
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zero point 8858 Right party. Uh, this time
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we're looking at a sample of 40 women, and
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now we need to find the probability that our sample
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mean that we find is within 10,000 of the mean
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for the women. So once again, we're going
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to find our standard deviation sampling distribution. That's gonna
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be this time. We're looking at the statistics for
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the women. So this is going to be 25,000
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over square root of 40. Calculate that out.
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That's 3952.47 are Sorry. 847 Anyway, let's find
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a Z lowers the upper. So the els you
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again. That's gonna be negative. 10,000 over our
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standard deviation of the sampling distribution for women. This
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one's gonna be 10,000 positive. So these are equal
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negative. 2.53 2.53 respectively. This is P.
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L. Looking at our table Once again, this
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lower probability is from zero point 0057 Upper probability 0.9943
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Finding a probability, which is probability Oper minus probability
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, lower. You get, um, zero point
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9886 part C s us two compared these to given
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explanation why one is higher than the other. And
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we see that part. He is greater. This
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is because standard deviation for men is greater then that
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for women I'm gonna have to move that up on
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. And because the standard deviation is greater, this
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means that this is a small This is smaller relative
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to our standard deviation, which means this let fewer
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standard deviations away from the mean, as opposed to
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this. All right, I'm gonna move to a
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different page party. Now we have sample of 100
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men. We want to find the probability that air
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sample mean is within. Ah, I believe it
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is sorry. It's not within this time. We
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need to find a sample mean that is greater than
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our population mean minus 4000. All right, so
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let's find our sampling distribution. Ah, standard deviation
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. So that's referring back to hear. That's 40,000
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square root of 100 square. 100 is tense.
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And this just 4000. All right, now we
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just see score for 4000 against 4000. So this
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could be because we are looking at 4000 less than
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the mean That's gonna be negative. 4000 top standard
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deviation is 4000. So this is negative 1.0 And
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if we look at our table, this corresponds to
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a probability is zero point 1587 and there you have
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it.