Chapter 9 Section 1

The Idea of Statistical Inference
“How often would this method give the correct answer if I used it very many times?”

With a partner…
Do Activity 9A on page 562

Parameter vs. Statistic

Parameter vs. Statistic

Parameter or Statistic?
The Tennessee STAR experiment randomly assigned children to regular or small classes during their first four years of school. When these children reached high school, 40.2% of blacks from small classes took the ACT or
SAT college entrance exams. Only 31.7% of blacks from regular classes took one of these exams.
Answer: Both p = 40.2% and p = 31.7% are statistics.

Parameter or Statistic?
A random sample of female college students has a mean height of 64.5 inches, which is greater than the 63-inch mean height of all adult American women.
Answer: The sample statistic mean x = 64.5 inches is a statistic, and the population mean µ = 63 inches is a parameter.

p vs. p
Population proportion: p
Sample proportion: p (p-hat)
Used to estimate the population proportion p
Note: Typically,
*English letters are used for statistics (x, s, r, etc.)
*Greek letters are used for population (µ, σ, α, β)

Sampling Variability
The value of a statistic varies in repeated random sampling
When we take many samples, this no longer is an issue

What if we can’t take every possible sample?
Note: A simulated sampling distribution is not the same as the actual sampling distribution.

The Bias of a Statistic
In other words, there is no systematic tendency to overestimate or
Underestimate the parameter.

Two Unbiased Sampling
Distributions

Bull’s Eye Try #1

Bull’s Eye Try #2

Bull’s Eye Try #3

Bull’s Eye Try #4