Sample Inferences

10.4 Making Inferences with Sample Surveys


Obj: SWBAT use sample surveys to make conclusions about populations.

Margin of error: The maximum expected difference between a sample result and a population parameter it is estimating.

Parameter: Characteristic to describe entire population.
Statistic: Characteristic to describe a sample.

Population: The collection of all data

Sample: A subset of a population (part of a population)

Vocab

Multiple Choice

Identify the population of the following: In the United States, a survey of 2184 adults ages 18 and over found that 1328 of them own at least one pet.

• 2184 adults ages 18 and over

• All adults

• Adult ages 18 and over

• Anyone 18 and older

Estimating Population Proportions

Looking at the first two surveys, you would predict that candidate A will not win the election.

As the sample size increases, the estimated votes approach 59%. Since 59% is more than 50%, there is a good chance candidate A will win.

THE GREATER THE SAMPLE SIZE, THE MORE ACCURATE THE DATA TENDS TO BE.

​Sample Size	​Candidate A Votes	​Percent of Votes for A in the Sample size
​5	​2	​40%
​12	​4	​33.3%
​20	​12	​60%
​30	​17	​56.7%
​50	​29	​58%
​125	​73	​58.4%
​150	​88	​58.7%
​200	​118	​59%

Margin of Error

In a survey of 1500 residents of a city, 47% said they eat organic foods. The margin of error is plus or minus 2.6%.

We need to take the statistic and add/subtract the MOE.

47% - 2.6% = 44.4% 47% +2.6% = 49.6%

It is likely that the exact percent of residents in the city who regularly eat organic foods in between 44.4% and 49.6%.

Multiple Choice

A survey says that 75% of students turn their homework in on time. There is a margin of error of 5%. What is the likely exact percentage of students who turn their homework in.

• 70%

• 70% - 80%

• 80%

• 75%