In chapters 18-19, we can only use the techniques on small samples if we believe the underlying popluation distribution is normal. And sometimes the only information we have about the population distribution is the data in the sample.
That's not really adequate to say whether it's reasonable to assume the population is normally distributed. Sometimes it might be adequate to be clear that the population is NOT normally distributed.
In order to get a feeling for this, you simply need to look at a lot of graphs of small datasets from normal populations in order to see what shapes they can have. After that, look at a lot of graphs of small datasets from a very strongly skewed population and see what shapes they have.
You can explore this too. Here's how I made these:
Here is a MINITAB Project with ten histograms of small data sets (11 observations) each of which is a random sample from a normal distribution. Save this file to your desktop and then open it in MINITAB and look through the histograms quickly. Notice how different they can be.
If you're interested in producing graphs like this yourself, use
Calc > Random Data > Normal
For this project, I made ten columns of 11 observations each, from a distribution with mean 3 and standard deviation 1.
Then I chose Graph > Histogram . Here I chose to use simple histograms, and in the dialog box, I chose "Multiple Graphs" and in the resulting box, I chose "Separate Graphs."
Now, to pursue this further, I created a different MINITAB Project for a skewed population distribution where I also used samples of size 11 from a population with a chi-squared distribution with 1 degree of freedom. A picture of the frequency curve for that distribution in our text in the chapter near the end of the book on inference in two-way tables. Notice that the histograms here mostly are skewed to the right and some have clear outliers on the right.