For example, a question that is of current interest on campus is, "Are
students willing to buy a computer which will be paid for by an increase
in tuition?" The population here is all students at WMU. Now if we knew
the population we would know how many students (what proportion) are willing
to have an increase in tuition to offset the purchase of a computer. And
this could be done, but it will take time (read as MONEY) to gather this
In an attempt to answer this question we obtain a random sample from the population. By random sample (here we go again) we mean
Another question along these lines is: "What's the family income of a student (or more specifically, the income paying the student's tuition)?" We mean of course the population distribution of the family incomes of all the students. We could use our sample to estimate this. Actually the histogram of the family incomes of the sample students is our estimate of the population distribution of the family incomes of all the students. From working with histograms, though, you know that we need quite a large sample to estimate this population distribution accurately. We could rephrase the question as: "What's the average family income of a student (or more specifically, the average income paying the student's tuition) ?" Then our sample average would be an estimate of the population average. Again, the question we must answer is: How much did our estimate miss by? We need an estimate of error of estimation.