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Chapter 12

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Chapter 12

Sample Surveys

- Population- all exp. units that you want to make a conclusion about
- Sampling frame – list of individuals from whom the sample is drawn. Not always the population of interest.
- Sample- small group of the population that you do an experiment/study on.

◦Parameter

-Describes the population

-Fixed Value

-Often Unknown

◦Statistic

-Describes the sample of a population

-Changes from sample to sample

-Use repeated samples/experiments to estimate the value of the parameter

Sample is said to be representative if the statistics accurately reflect the population parameters

EXAMPLE 1:

A polling agency takes a sample of 1500 American citizens from a list of tax returns and asks them if they are lactose intolerant. 12% say yes. This is interesting, since it has been shown that 15% of the population is lactose intolerant.

12% = _________15% = __________

Population? Sampling frame? Sample?

EXAMPLE 2:

A random sample of 1000 people who signed a card saying they intended to quit smoking were contacted a year after they signed the card. It turned out that 210 (21%) of the sampled individuals had not smoked over the past six months.

21% = _________

Population =

Sampling frame=

Sample =

Parameter of interest =

EXAMPLE 3:

On Tuesday, the bottles of tomato ketchup filled in a plant were supposed to contain an average of 14 ounces of ketchup. Quality control inspectors sampled 50 bottles at random from the day’s production. These bottles contained an average of 13.8 ounces of ketchup.

14 = _________13.8 = __________

Population? Sample? Sampling frame?

EXAMPLE 4:

A researcher wants to find out which of two pain relievers works better. He takes 100 volunteers and randomly gives half of them medicine #1 and the other half medicine #2. 17% of people taking medicine 1 report improvement in their pain and 20% of people taking medicine #2 report improvement in their pain.

17% = _________20% = __________

Population? Sampling frame? Sample?

Some more vocab….

Bias VS. Variability:

* Bias- consistent, repeated measurements that are not close to the population parameter

* Variability- basically like reliability

* We want to keep both of these low!

* To reduce bias… use random sampling

* To reduce variability… use larger samples!

SAMPLING VARIABILITY

* Different samples give us different results

* Different size samples give us different results

* Bigger samples are better!!

* Sampling distribution: If we take lots of samples of the same size and make a graph

True parameter

* Variability = spread/width of graph

Larger samples give smaller variability:

Lots of samples of size 100

Lots of samples of size 1000

True parameter

True parameter

- Bias is the accuracy of a statistic
- Variability is the precision of a statistic

Label each as high or low for bias and variability

True parameter

True parameter

True parameter

Label each as high or low for bias and variability

True parameter

True parameter

Another vocab word…

- Unbiased Estimator:

- When the center of a sampling distribution (histogram) is equal to the true parameter.

True parameter

GOOD Sampling Designs:

1) Simple Random Sample (SRS) - Every experimental unit has the same chance of being picked for the sample and every possible sample has the same chance of being selected

- Give every subject in the population a number
- Use the table of random digits and read across to select your sample
- Ignore repeats

EXAMPLE:

Take an SRS of 5 from the following list. Start at line 31 in the table.

SmithJonesHolloway

DeNizzoDavidAdams

SchaeferGrayCapito

MeyersGingrichCard

DietrichMorelandHall

WalshWhitterJordan

EXAMPLE:

Take an SRS of 4 from the following list. Start at line 18 in the table.

McGloneMcCuenWilson

SzarkoBellavanceWoodring

StotlerKellyWheeles

TimminsArdenMcNelis

GemgnaniO’BrienRobinson

LorenzLakeBainbridge

Stratified Random Sample:

(NOT simple random sample)

- Divide population into groups with something in common (called STRATA)
- Example: gender, age, etc.

2) Take separate SRS in each strata and combine these to make the full sample

- can sometimes be a % of each strata

Example:

We want to take an accurate sample of CB South students. There are 540 sophomores, 585 juniors, and 530 seniors. Take a stratified random sample.

GOOD Sampling Methods (continued):

3) Systematic Random Sample – The members of a population are ordered in some manner. The first member is selected at random. Each additional member is selected at a predetermined interval.

Examples:

- Surveying every 5th person that walks thru the back door of CB South.
- Selecting a random person to start with (like person #4) and then taking every 10th person on the list after that (person #14, person #24, person #34, etc.)

- Cluster Sample – Population is broken into groups. All members in one or more groups are taken as the sample.
- Multistage Sample - - Sample from a big group
- Within each part of that sample, take another sample

- Within each part of that sample, take another sample

Example:

The government wants to survey the entire population. However they cannot just give every person a number and do an SRS. So they follow this process:

* Randomly select 5 counties from each state

* In each of those counties, randomly select 6 towns/cities

* In each town/city, randomly select 4 streets

* On each street, select 3 houses, and interview the head of the household.

BIASED SAMPLING METHODS:

- Voluntary Response Samples
- Chooses itself by responding to a general appeal.
- Call-in, write-in, stopping in the mall, etc.

- Convenience Samples
- Selecting individuals that are the easiest to reach/contact

JUST CHECKING

We need to survey a random sample of 30 passengers on a flight from San Francisco to Tokyo. Name each sampling method described below:

- Pick every 10th passenger that boards

- From the boarding list, randomly choose 5 people flying first class, and 25 of the other passengers

- Randomly generate 30 seat numbers and survey the passengers who sit there

- Randomly select a seat position (right window, left window, right aisle, etc.) and survey all people in those seats