Aim: What are the confidence intervals and samples size for proportions?

1. Aim: What are the confidence intervals and samples size for proportions? Quiz Friday

2. Proportions • Proportions: represents a part of a whole • Can be expressed as a fraction, decimal or percentage • Can also be represented as probabilities • Proportions can be obtained from samples or populations

3. Proportion Symbols • p = populations proportions (read “p hat”) = sample proportions For sample proportion,

4. Example • In a study, 200 people were asked if they were satisfied with their job or profession; 162 said that they were • In this case n = 200 and X = 162, then

5. Confidence Intervals • To construct confidence intervals about a proportion, one must use the maximum error of estimate, which is

6. Confidence Interval for Proportions

7. Rounding Rule for Confidence Interval for a Proportion • Round off to three decimal places

8. Example • A sample of 500 nursing applications included 60 from men. Find the 90% confidence interval of the true proportion of men who applied to the nursing program. • Solution:

9. Sample Size for Proportions • To find the sample size needed to determine a confident interval about a proportion, use this formula (if necessary round up to a whole number):

10. Class Work • In a recent study of 150 households, 54 had central air conditioning. Find • A survey of 200,000 boat owners found that 12% of the pleasure boats were named Serenity. Find the 95% confidence interval of the true proportion of boats named Serenity.

11. Class Work 3. A researcher wishes to estimate, with 95% confidence, the proportion of people who own a home computer. A previous study shows that 40% of those interviewed had a computer at home. The researcher wishes to be accurate within 2% of the true proportion. Find the minimum sample size necessary.