8.3 Estimating Population Proportions LEARNING GOAL Learn to estimate population proportions and compute the associated margins of error and confidence intervals. Page 355

The Basics of Estimating a Population Proportion Page 355 Slide 8.3- 2

95% Confidence Interval for a Population Proportion For a population proportion, the margin of error for the 95% confidence interval is where is the sample proportion. The 95% confidence interval ranges from – margin of error to + margin of error We can write this confidence interval more formally as Page 356 Slide 8.3- 3

EXAMPLE 1 TV Nielsen Ratings The Nielsen ratings for television use a random sample of households. A Nielsen survey results in an estimate that a women’s World Cup soccer game had 72.3% of the entire viewing audience. Assuming that the sample consists of n = 5,000 randomly selected households, find the margin of error and the 95% confidence interval for this estimate. Solution: Page 356 Slide 8.3- 4

Choosing Sample Size Choosing the Correct Sample Size In order to estimate a population proportion with a 95% degree of confidence and a specified margin of error of E, the size of the sample should be at least n = 1 E 2 Pages 357-358 Slide 8.3- 5

EXAMPLE 2 Minimum Sample Size for Survey You plan a survey to estimate the proportion of students on your campus who carry a cell phone regularly. How many students should be in the sample if you want (with 95% confidence) a margin of error of no more than 4 percentage points? Solution: Page Slide 8.3- 6