~Some teachers & textbooks do make a distinction between these.

~Our book does, so I will explain this difference in simple terms.

~Say you want a sample of n from a population size of N. For example, you want to choose 50 data points from a population  size of 1,000 of these data points. In this case, n=50 & N=1,000.

~To get a Random sample of 50, each data point in the population must have an Equal Chance of being selected.

~To have a Simple Random sample of 50, every group of 50 data points must have an Equal Chance of being selected.

~As an illustration, let's take the example of selecting 10 students from a class of 60.  Let's assume there are 6 rows of seats in the classroom with 10 students in each row. I roll a die & use the result to choose a row (1-6).  Then I select all 10 students from that row for my sample.

~My sample is Random since every student in class has an equal chance of being selected. My die could give a result of 1, 2, 3, 4, 5, or 6.  So, every row has an equal chance of be selected, consequently, every student has an equal chance.

~However, my sample is Not Simple Random since every group of 10 students do not have an equal chance of being selected. For this example, 10 students coming from different rows cannot be selected.

~Basically, just remember when choosing randomly, every data point in the population must be equally likely to be chosen or have equal probabilities of being chosen.

~The TI-83 has a menu that will choose random integers (one at a time or in groups).  Use Math, PRB, move down to menu 5, enter, insert the lowest integer, comma, the highest integer, comma, then the number you want to choose.  Then press enter.  Every time you repeat pressing enter, you'll get more random results.

~This is great for choosing random samples, however, you must assign integers to your data points in your population before you use this technique.