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 =.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 = 1.03 n≈1111 Estimate the population size for each margin of error. 2) ±10%3) ±4%4) ±2%

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%