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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.

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6.3 Confidence Intervals for Population Proportions

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  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

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