When gathering data how do we get the best results?

Population—a group of people or objects that we want to get information about.

Examples: CHS Students US Citizens Georgia Teens Items produced at a Mfg. Plant

When gathering data how do we get the best results?

It is not always possible to gather information from the entire populationSample—a subset of a population.

Population

Sample

When gathering data how do we get the best results?

Given the population: 7, 3, 9, 3, 8, 7, 6, 4, 3, 2, 3

Select a sample of the population that contains 4 members.Examples:

When gathering data how do we get the best results?

Do samples chosen from a population always match? Explain your answer.

Do samples always reflect the true variation in a population? Explain your answer.

When gathering data how do we get the best results?

There are 4 methods of selecting samples that we need to be aware of:Types of Samples• self-selected—members of the population can volunteer to be in the sample.• systematic—a rule is used to select members from the population.• convenience—easy-to-reach members of the population are selected.• random—each member has an equal chance of being selected.

When gathering data how do we get the best results?

Self-selected, Systematic, Convenience, Random

Which method gives a sample most like the original population? Explain your thinking.

When gathering data how do we get the best results?

Unbiased sample—is a fair representation of the population you want information about.

Biased sample—under represents some part of the population you want information about.

When gathering data how do we get the best results?

Examples:You want to know the favorite high school subject of adults. You use the math teachers as your sample.

Population:

Sample:

Sample Type:

Biased or Unbiased?

When gathering data how do we get the best results?

Examples:Toyota wants to determine information about the 2011 Camry produced at the local factory. They select every 300th Camry produced.

Population:

Sample:

Sample Type:

Biased or Unbiased?

When gathering data how do we get the best results?

Newsweek wants to survey American voters about whether they approve or disapprove of congress.

Who is the population?Why will Newsweek need to select a sample?Which sample should Newsweek use (self-selected, systematic, convenience, random)? Explain your reasoning.

When gathering data how do we get the best results?

Will any sample ever match the original population perfectly? Explain your thinking.

Margin of Error—gives the limit on how much the responses of a sample will differ from the responses of a population.

When gathering data how do we get the best results?

You want to conduct a survey about high school students favorite movie. What is the population? You decide to select a random sample to get the best chance of unbiased results. Which sample size is most likely to have the smallest margin of error? Explain your thinking.Sample sizes:

10 25 50 100 300 500 1000

When gathering data how do we get the best results?

To calculate the margin of error we use the formula:

Calculate the margin of error a sample would give if it had the following size:

10 25 50 100 300 500 1000

When gathering data how do we get the best results?

The margin of error is applied to the results found from the sample group and gives a range that should accurately reflect the results that would be given by the entire population.Example:A survey of 900 high school students found that 42% read less than 10 books per year. What interval is likely to contain the actual percentage of high school students that read less than 10 books per year?

Margin of Error and Sample SizeWhat sample size would be

needed to have a margin of error smaller than + 5%?

What sample size would be needed to have a margin of error smaller than + 1%?