Chapter 21: The Accuracy of Percentages The Bootstrap When we do - - PowerPoint PPT Presentation

Chapter 21: The Accuracy of Percentages

The Bootstrap When we do not know what is in the box, we estimate the SD of the box by pretending the box looks just like the sample. Confidence Intervals A 95% confidence interval for the population percentage is given by Sample percentage ± 2 (SE%) The confidence interval is valid if the number of draws is large enough.

Example 1. A nutrition student takes a random sample of 300 people from Cache Valley and finds that 89 of them say they eat beef at least twice a week. a) Estimate the percentage of people in Cache Valley who eat beef at least twice a week. b) Find an approximate standard error of the percentage. c) Find a 95% confidence interval for the percentage of people in Cache Valley who eat beef at least twice a week.

Example 2. Lemons are premium-grade, table-grade, or juice-grade. A farmer takes a simple random sample of 500 lemons from a large crop and finds that 75 are juice-

• grade. Find a 95% confidence interval for the percentage
• f juice-grade lemons in the crop.

For a confidence interval with a different confidence level, normal tables are used to find the multiplier. e.g. an 80% confidence interval is Sample percentage ± 1.3 (SE%) e.g. a 90% confidence interval is Sample percentage ± 1.65 (SE%)

Example 3. A health inspector takes a random sample of 300 10-year-olds in a city, and finds that 73% of them have had chicken-pox. Find a 90% confidence interval for the percentage of 10-year-olds in the city who have had chicken-pox.