Using the Range Rule of Thumb to find significant values

Intro

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to use the Range Rule of Thumb to find significant values.  Here's our problem statement: The accompanying table describes results from groups of 10 births from 10 different sets of parents.  The random variable x represents the number of girls among 10 children.  Use the Range Rule of Thumb to determine whether one girl in 10 births is a significantly low number of girls.

Part 1

OK, so the first part of this problem is asking us to determine the maximum value using that Range Rule of Thumb.  To do that, let's actually come down here and click on this icon to view the table of our data.  And we do that and find that here we have a probability distribution.  We can easily get the mean and standard deviation to use for our Range Rule of Thumb by dumping this data into StatCrunch.  So I’m going to click this icon right here and dump my data into StatCrunch.  Great.  Now we’re going to resize his window here so we can see more of what's going on.  Excellent!

OK, so we need to get the mean and standard deviation for this distribution.  Now if I go directly into Stat –> Summary Stats and then Grouped/Binned Data, I’m going to find that I'm going to get frustrated because this option requires us to have integer values; it wants frequency counts here.  What we have are percentages because it's a probability distribution.  So what I need to do here is provide integers.  And the easiest way to do that is to round each of these probabilities which are really percentages — multiply by 100 and then round to the nearest integer.

So if I do that here for this first column, I'm gonna find I get 0.4 because I move that decimal point to places to the right.  That gives me 0.4, which rounds down to zero.  The next value I get — move it over two places — 1.1, so that’s going to round to 1.  And I just keep doing the same thing for each of the numbers here in my probability distribution.

OK, now that I actually have counts here, I'm going to go into Stat –> Summary Stats –> Grouped/Binned Data.  The bins are going to be your x-values; that’s your random variable.  The counts are going to be what we just calculated in the new column there.  I want the mean and the standard deviation.  There is my mean and standard deviation.

So now all I need to do is apply the Range Rule of Thumb, come back over here, and get my maximum value.  So to do that, I whip out my calculator.  I’m going to take the mean value, which in this case is 5.14, and add it to twice the standard deviation.  I don’t need to type the whole number in because I'm only asked to round to one decimal place, so this four decimal places should be more than sufficient.  And there’s my maximum value.  I round to one decimal place.  Fantastic!

Part 2

Now, the second part asks us for the minimum value.  I’m going to do the same thing — use the mean and standard deviation, make the same calculation, only this time I’m going to subtract everything out.  So there's the mean value, 5.14, subtracting out twice the standard deviation.  Round to one decimal place.  Good job!

Part 3

Now, the last part asks, “Based on the result, is one girl in 10 births a significantly low number of girls?  Explain.”  Well, if its’ going to be significantly low, that's means it’s outside the range of usual values on the low side.  So what we’re really looking for is something outside this range on the low side, which would be less than the minimum value.  1 is less than our minimum value of 1.7, so we conclude, yes, this is a significantly low number girls.  So I want yes, it's significantly low because it's less than the minimum value that's not significant.  Excellent!

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