Introduction

The beginning of a study is formed by a question . This question usually defines the population  (or populations) of interest. If we knew the population then we could answer the question.

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 information.

In an attempt to answer this question we obtain a random sample from the population. By random sample  (here we go again) we mean

1.

The items in the sample are independent of one another.

2.

Conditions do not change as the sample is gathered.

With regards to the question on the cost of a computer, we would select n students at random and ask them the above question. The number who answer yes divided by n would be our estimate of the true proportion. As usual, the question we must answer is: How much did our estimate miss by? That's the topic of this chapter.

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.