This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Chapter 3 Estimation of p 3.1 Point and Interval Estimates of p Suppose that we have BT. So far, in every example I have told you the (numerical) value of p . In science, usually the value of p is unknown to the researcher. In such cases, scientists and statisticians use data from BT to estimate the value of p . Note that the word estimate is a technical term that has a precise definition in this course. I dont particularly like the choice of the word estimate for what we do, but I am not the tsar of the Statistics world! It will be very convenient for your learning if we distinguish between two creatures. First, is Nature , who knows everything and in particular knows the value of p . Second is the researcher who is ignorant of the value of p . Here is the idea. A researcher plans to observe n BT, but does not know the value of p . After the BT have been observed the researcher will use the information obtained to make a statement about what p might be. After observing the BT, the researcher counts the number of successes, x , in the n BT. We define p = x/n , the proportion of successes in the sample, to be the point estimate of p . For example, if I observe n = 20 BT and count x = 13 successes, then my point estimate of p is p = 13 / 20 = 0 . 65 . It is trivially easy to calculate p = x/n ; thus, based on your experiences in previous math courses, you might expect that we will move along to the next topic. But we wont. What we do in a Statistics course is evaluate the behavior of our procedure. What does that mean? Well, recall that in first lecture I stated that statisticians evaluate procedures by seeing how they perform in the long run . We say that the point estimate p is correct if, and only if, p = p . Obviously, any honest researcher wants the point estimate to be correct. Lets go back to the example of a researcher who observes 13 successes in 20 BT and calculates p = 13 / 20 = 0 . 65 . The researcher schedules a press conference and the following exchange is recorded. Researcher: I know that all Americans are curious about the value of p . I am here today to announce that based on my incredible effort, wisdom and brilliance, I estimate p to be 0.65. 23 Reporter: Great, but what is the actual value of p ? Are you saying that p = 0 . 65 ? Researcher: Well, I dont actually know what p is, but I certainly hope that it equals 0.65. As I have stated many times, nobody is better than me at obtaining correct point estimates. Reporter: Granted, but is anybody worse than you at obtaining correct point estimates? Researcher: (Mumbling) Well, no. You see, the problem is that only Nature knows the actual value of p . No mere researcher will ever know it....
View
Full
Document
This note was uploaded on 10/23/2009 for the course STAT STATS 371 taught by Professor Professorwardrop during the Fall '09 term at Wisconsin.
 Fall '09
 ProfessorWardrop
 Statistics

Click to edit the document details