Making Statistical Inferences

What is a “statistic”? A population may have one or more properties that we can quantify. In general this is unknown to us - we call this underlying property a parameter of the population. When we measure this parameter by using a Simple Random Sample (SRS) – we have measured a statistic

Sampling Variability Repeated measurements of a statistic do not yield the same value – sampling variability SRS should eliminate bias Sampling variability is predictable

Bias and Variability Low bias, high variability High bias, low variability Low bias, low variability High bias, high variability

Controlling Variability Choose a sufficiently large n to give an acceptable amount of variability A large n will usually give a smaller amount of variability (assuming a truly SRS) – look at example 3.22

Population Size Doesn’t Matter! As long as the population is at least 100 times larger than the “n” of the sample – size of the population does not affect variability A sample of 100 out of a population of 10 000 will have essentially the same amount of variability as a sample of 100 out of a population of 1 million. In other words – the two samples will yield equally precise estimates for a parameter.

A “non-random” sample of questions… Example 3.23 Problems: 3.62, 3.66, 3.70, 3.71 Link to applets…

In conclusion… Make sure you understand the distinction between parameter and statistic Know what is meant by bias and variability Try 3.59, 3.69, 3.91