1. Making Statistical Inferences

2. 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

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

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

5. 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

6. 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 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.

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

8. 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