Finding probability by subjective judgement

Intro

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to find probability by subjective judgment.  Here's our problem statement: Assume that 700 births are randomly selected and 341 of the births are girls.  Use subjective judgment to describe the number of girls as significantly high, significantly low, or neither significantly low nor significantly high.

Solution

OK, we have four different options from which to choose.  How do we know which option is the correct one?  Well, we're looking at births, and a birth could be either a boy or a girl.  So we would expect that the number of births that are girls would be approximately half of the total amount, because there's approximately a 50% chance of having a birth be a girl if everything is truly randomly selected.  So we would expect about half of the 700 to be girls.  And indeed, we see that 341 is around 350, which is half of 700.  So we would say, yes, that the number of girls is neither significantly low nor significantly high.

Alternative

Another way to get the answer is to actually use your calculator.  I know it says “subjective judgment,” but we can actually run the numbers out.  The probability from this sampling is the part over the whole.  So we have the part, which is 341, and divided by the whole, which is 700, and here we've got a little bit more than 48% of the the sample here are girls.  This is around 50%, so again we would say that the number of girls is neither significantly low nor significantly high.

How far away could you get from that 50% expected probability before you start saying, “OK, so now the difference is statistically significant”?  Well, you need a standard to go by, and the standard that's typically used is 5%.  There is no mention in the problem statement of what standard to use because they want you to use subjective judgment.  However, in those cases where they don't mention anything, it's by and large your best bet to just use the standard that is by and far the most commonly used, and that is 5%.

So here we see we're expecting 50%.  We have a little more than 48%, so if you subtract that out, you're gonna get less than 5%.  So we're within that 5% margin, and so we would say that, yeah, this is within what we would expect to see; it's not significantly low or significantly high.  Well done!

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