1 / 8

6.3 Confidence Intervals for Population Proportions

6.3 Confidence Intervals for Population Proportions. Find a point estimate for a population proportion Construct a confidence interval for a population proportion Determine the minimum sample size required when estimating a population proportion.

paco
Download Presentation

6.3 Confidence Intervals for Population Proportions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. 6.3 Confidence Intervals for Population Proportions Find a point estimate for a population proportion Construct a confidence interval for a population proportion Determine the minimum sample size required when estimating a population proportion

  2. The point estimate for p, the population proportion of successes, is given by the proportion of successes in a sample and is denoted by where x is the number of successes in the sample and n is the sample size. The point estimate for the population proportion of failures is q = 1 – p. The symbols p and q are read as “p hat” and “q hat.” Point estimate for p

  3. Try it yourself 1 • Finding a Point Estimate for p In a survey of 1006 U.S. adults, 181 said that Abraham Lincoln was the greatest president. Find a point estimate for the population proportion of U.S. adults who say Abraham Lincoln was the greatest president. 0.180

  4. A c-confidence interval for a population proportion p is where The probability that the confidence interval contains p is c. C-Confidence interval for a population proportion p

  5. Try it yourself 2 • Constructing a Confidence Interval for p Use the data given in Try It Yourself 1 to construct a 90% confidence interval for the population proportion of U.S. adults who say that Abraham Lincoln was the greatest president. 90% CI ( 0.160, 0.200)

  6. Try it yourself 3 • Constructing a Confidence Interval for p The graph shown is from a survey of 498 U.S. adults. Construct a 99% confidence interval for the population proportion of adults who think that people over 65 are the more dangerous drivers. 99% CI ( 0.20, 0.30)

  7. Given a c-confidence level and a margin of error E, the minimum sample size n needed to estimate p is This formula assumes that you have preliminary estimates of p and q. If not use p = 0.5 and q = 0.5. finding a minimum sample size to estimate p

  8. Try it yourself 4 • Determining a Minimum Sample Size You wish to estimate, with 90% confidence, the population proportion of females who refuse to eat leftovers. Your estimate must be accurate within 2% of the population proportion. Find the minimum sample size needed if (1) no preliminary estimate is available and (2) a previous survey found that 11% of females refuse to eat leftovers. n = 1692 n = 663

More Related