Chapter 3 Stats

Parameter

A number that describes the population, in practice we usually don’t know the parameter.

Statistic

A number that describes a sample, and may change between different samples. It is often used to estimate an unknown parameter.

We use ________ to estimate __________.

We use statistics to estimate parameters

P

Population proportion(a parameter), P=(# of individuals in category)/(# in whole population)

p̂(p hat)

Sample proportion(a statistic), p̂=(# of individuals in sample category)/(sample size)

Bias in regards to parameter

Bias, where our sample systematically over or under estimates the parameter

Variability

Describes how our statistic changes from sample to sample, if a result has low variability, repeated polls would yield similar results. High variability would mean you would get different results after repeated trials.

Confidence Intervals

Due to variability, it is wise to report a range rather than a single value.
Margin of error tell us how wide the range should be.

Range is called a confidence interval.

Confidence level

used to describe how sure we are that the parameter is in the interval, 95% is commonly used.

Balance between margin of error and confidence level

Having a really high confidence level doesn’t help if the margin of error is really high
Conversely, having a really small margin of error isn’t helpful if the confidence level is low.

3 things to pay attention to

Margin, what happens to it if we increase sample size?
If we have a fixed sample size and decrease our margin, what happens to our confidence level?

If we have a fixed sample size and increase our confidence level, what happens to the margin?