Working with Samples:

Sample- a sample gathers information from only part of a population.

Sample Proportion- is the ratio of the number of times an event occurs in a sample to the size of the sample. x/n, x=times it occurs, n=size of sample

Examples:Find the sample proportion.1) In a sample of of 350 teenagers, 294 have never made a snow sculpture. Find the sample proportion for those who have never made a snow sculpture.

294

350= .84 or 84%

2) In a poll of 1085 voters, 564 favor Candidate A. Find the sample proportion for those who favor Candidate A.

52%

A sample proportion should be reported with an estimate of error, called the margin of error.

When a random sample of size n is taken from a large population, the sample proportion has a margin of error of approximately ± 1

√n

Examples:1) A poll reports that 56% of voters favor Candidate B, with a margin of error of ±3%. Estimate the number of voters in the poll.

margin or error= ± 1

√n

.03 = ± 1 √n

√n√n

√n = 1 .03

n≈1111

Estimate the population size for each margin of error.2) ±10% 3) ±4% 4) ±2%

100 625 2500

Examples:Find the margin of error for the sample and find the interval likely to contain the true population percentage.

1) A survey of 2580 students found that 9% are left-handed.

margin of error= ± 1

√n= ±.0197 ≈ ±2%

9%7% 11%

-2% +2%

The proportion of students who are left handed are between 7%-11%.

2) In a poll of 123 students, 87 have never ridden a ferry. Find the sample proportion, the margin of error, and the interval likely to contain the true population proportion.

71%, ±9%, 62%-80%