6.3 Confidence Intervals for Population Proportions The fun continues…

Point Estimate for the Population Proportion p Remember p from a binomial experiment is the probability of success? This is also called the population proportion. p = x x = number of successes n n = total # in sample p = point estimate for population proportion

Example 1 In a survey of 3859 adults from the U.S., 1177 said that of all the presidents from the 20th century, Franklin D. Roosevelt was the greatest. Fins a point estimate for the population proportion of adults who agree.

Confidence Intervals for a Population Proportion p  

Steps to construct the interval Identify n and x Find the point estimate Verify you can approximate to the normal distribution Find the critical value zc Find the margin of error Find the endpoints

Example 2 Use the data from example 1 to construct a 90% confidence interval for the proportion of adults who say Roosevelt was the greatest president of the 20th century. Recall, x= 1177 and n = 3859 INTERPRET your results!

Example 3 (with calculator) From a survey of 900 adults, construct a 99% confidence interval for the proportion of adults who think that people over 75 are the most dangerous drivers. (33% according to graph) STAT – Tests A:1-PropZInt x = .33 x 900 n = 900

III. Increasing Sample Size to Increase Precision  

Example 4 You wish to estimate, with 90% confidence and within 2% of the true population, the proportion of adults age 18-29 who have high blood pressure. Find the minimum sample size needed if (1) no preliminary estimate is available and (2) a previous survey found that 4% of adults in this age group had high blood pressure.

Classwork/Homework Together p308 #3, 13, 25 Classwork p308 #4, 14, 26 Homework p308 #6-12 even, 27 Together p308 #3, 13, 21, 25 Classwork p308 #4, 14, 22, 26 Homework p308 #6-12 even, 24, 27