11.4 Select and Draw Conclusions from Samples

Population

A group of people or objects that you want information about

Sample

A subset of the population being studied

Unbiased sample

A sample that is representative of the population you want information about

Biased sample

A sample that overrepresents or underrepresents part of the population

Margin of error

The number that gives a limit on how much the responses of the sample would differ from the responses of the population

Example 1

Classify samples

School Lunch A teacher wants to survey everyone at her school about the quality of the school lunches. Identify the type of sample described and tell if the sample is biased.

a. The teacher surveys every 7th student that goes through the lunch line.

b. From a random name lottery, the teacher chooses 150 students and teachers to survey.

Solution

a. The teacher is using a _rule_ to select students, so the sample is a _systematic_ sample. This sample is _biased_ because the teacher surveys the students, but not the teachers.

b. The teacher chose from a random lottery, so the sample is a _random_ sample. The sample is _unbiased_ because both students and teachers are being surveyed.

MARGIN OF ERROR FORMULA

When a random sample of size n is taken from a large population, the margin of error is approximated by:

Margin of error = ±

This means that if the percent of the sample responding a certain way is p (expressed as a decimal), then the percent of the population that would respond the same way is likely to be between p - and p + .

Example 2

1

Newspaper Survey In a survey of 1432 people, 26% said that they read the newspaper every day. (a) What is the margin of error for the survey? (b) Give an interval that is likely to contain the exact percent of all people who read the newspaper every day.

a.

1432

Margin of error = ± = ± » ±0.026__

The margin of error for the survey is about _±2.6_%.

b. To find the interval, add and subtract _2.6_%.

26% - _2.6_% = _23.4_%

26% + _2.6_% = _28.6_%

It is likely that the exact percent of all people who read the newspaper everyday is between _23.4_% and _28.6_%.

Example 3

Find a sample size

Community Survey A group of students survey the local community about their favorite beverage. How many people did they survey if the margin of error is ±7%?

Solution

Use the margin of error formula.

Margin of error = ±

_±0.07_ = ±

_0.0049_ =

n » _204_

About _204_ people were surveyed.