Create and interpret a normal quantile plot

Intro

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we’re going to learn how to create and interpret a normal quantile plot.  Here's our problem statement: Sample data for the arrival delay times in minutes of airlines flights is given below.  Determine whether they appear to be from a population with a Normal distribution.  Assume that this requirement is loose in the sense that the population distribution need not be exactly normal, but it must be a distribution that is roughly bell-shaped.

Solution

OK, here we’re going to click on this icon so we can get our data set.  There's our data, and I'm going to put this into StatCrunch.  Now I’ll resize this window so we can see better what's going on.  Alright, now my data is here in StatCrunch.

So to check for a Normal distribution, I could just rush off to do the QQ plot, but it’s actually smarter to just do the histogram first.  So I’m going to go to Graph –> Histogram, select my data, and then I want to check “Value above bar.”  Here’s my histogram.  Notice we have a skewed distribution — we don’t have the bell-shape — plus there's a couple of outliers here.  So already it doesn't look good, but I can go make my QQ plot to confirm this.

I go to Graph –> QQ Plot.  I select my data.  I’m going to select the box for “Normal quantiles on y-axis” because that’s how I’ve always seen the QQ plots.  I hit Compute! and notice how we get a distribution of our data points here that’s making what we would call a curvilinear shape.  So it’s not conforming to this straight line of best fit.  And the curvilinear shape actually conforms with the skewness of the distribution which we saw earlier in the histogram.

So it doesn’t look like we’re meeting the requirements for a Normal distribution.  So I’m not going to select answer options B and C.  Answer option A?  “No, because the histogram of the data is not bell-shaped” — that’s true — “there is more than one outlier” — true — “and the points of the normal quantile plot do not lie reasonably close to a straight line.”  That’s probably what we want, but let’s check out answer option D just to be safe.  “No, because the histogram is bell-shaped, there’s less than two outliers” — no, that’s not going to be the one we want, so we want answer option A.  Well done!

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