Sampling

Population vs. Sample• Population – The entire group you want to

study• Sample – The portion of the population you

select to study• Parameter – Fact about a population• Statistic – Fact about the sample• Parameter : Population :: Statistic : Sample• The theory of sampling is the statistic should

be the same or at least close to the parameter

Bad Sampling• Read Example 5.1 on page 202• The design of a statistical study is biased if it

systematically favors certain outcomes• Voluntary response sampling is when you have

people contact you to answer your survey. It’s biased because people with strong opinions for change are the most likely to go out of their way to contact you.

• Convenience sampling is when you pick individuals that are easy to reach. It is biased because they often have many lurking variables in common that made them easy to reach.

Bad Sampling• Who likes going to the mall?• Read example 5.2 on page 204• Who doesn’t want kids?• Read example 5.3 on page 204

Good Sampling• A simple random sample (SRS) means

everyone in the population has an equal chance of being selected.

• The best way to be fair is to be random. Assign everyone in the population a number, then randomly draw numbers and interview the people whose number was drawn.

Is it random?• Pick a random number.• Was it really random or are there some numbers

you’re more likely to pick than others?• Dangers of physical mixing: Read Application 5.1

on page 215• In Excel, =rand() creates a random number

between 0 and 1– How would you have excel generate a random

number between 0 and 100?• =100*rand()

Population vs. Sample Ideally• Ideally the statistic sample is the same as the

population parameter

• Parameter = Percent =Statistic

Population 100%Sample

Population vs. Sample Actually• In reality the statistic is a close approximation

to the parameter, but doesn’t equal it.• Assuming the sample isn’t biased, we can use

the following equation to calculate a 95% confidence interval

– p is the percent result from the statistic• Be consistent on the decimal or percentage versions

– n is the sample size

95% Confidence Interval• Add and Subtract to the

statistic, p

• This creates a range that you are 95% confident contains the true population parameter– There is a 95% chance that the true value is within

that range

Class Survey: Dominant Hand

• Sample Size = 123Left = 11%, Right = 85%, Ambidextrous =

5%Why does it add up to 101%?

Round off Error

We are 95% confident that between 5% and 17% of Saint Joe students are left handed.

Probabilistic LanguageYou are never 100% sure of anything

Assuming the sample wasn’t biased, we are 95% confident that the handedness of St. Joe students falls in these ranges.

Confidence Interval Example• If you calculate your 95% confidence interval to

be 1%, your actual error could be larger. That 1% is what we call a confidence interval. You are 95% confident that the error between your measured result and the actual result is 1%.

• If the results from your study show that the percent of Americans that believe in Heaven is 88 + 5%, what that means is you are 95% confident that between 83% and 93% of the population believes in Heaven.