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Confidence intervals for proportions

This guide outlines the steps to construct a 95% confidence interval for population proportions. It details the importance of the sample size and the calculation of the standard error, especially when using a sample proportion in the absence of a known population proportion. The process includes finding the Z-score corresponding to the desired confidence level, calculating the margin of error, and determining the confidence interval range. Examples include estimating the proportion of American households serving cranberries and deriving a confidence interval for the population of altered dogs.

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Confidence intervals for proportions

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  1. Confidence intervals for proportions Sec 9.3

  2. The Plan; For building a 95% confidence interval

  3. The Plan;For building a 95% confidence interval What do we use for (se)

  4. What to use for Standard Error, • The standard error for a sampling distribution of proportions is normally; • Sense we don’t know p we will use instead, where is our sample proportion. • This will give us a strong approximation for the true standard error.

  5. The Plan;For building a 95% confidence interval

  6. The Plan;For building a 95% confidence interval • In general: For proportional data • Our confidence interval is found by finding; Z-score for confidence level Sample proportion Standard Error or

  7. Reminder about sample size; • Since we are working with proportional distributions we need to be sure that our sample size is large enough for the central limit theorem to give us a normal distribution to work with. • The sample size must be large enough so that; and

  8. Lets try; 73.5% of Americans have cranberries at thanksgiving. .735 You are tasked with finding out the proportion of American households that will have cranberries with their Thanksgiving meal. Step one: Find a point estimate Step two: Build a 95% confidence interval

  9. Lets try; 73.5% Step One: Using a sample you randomly survey 100 American and find that 70 of plan on having cranberries. This gives you a point estimate of .7000

  10. Lets try; 73.5% Step Two: We need to find the standard error in order to build our intervals.

  11. Lets try; 73.5% Step Two: We need to find the standard error in order to build our intervals.

  12. Lets try; 73.5% Step Two: We need to find the standard error in order to build our intervals. So our interval is; Margin of error The interval from 61.02% to 78.98%

  13. Lets try; 73.5% Therefore we are 95% confident that between 61% and 79% of Americans will be having cranberries with their Thanksgiving meal.

  14. You Try; • A sample of 1500 dogs finds that only 1037 of them are “altered”. Find a 95% confidence interval for the population proportion of altered dogs.

  15. Other confidence Levels: We can find confidence intervals with other confidence levels. The most common are 90%, 95%, and 99%. The only difference is the z-score we will use needs to be changed to model the new confidence level. Here are the z-scores for these common confidence levels

  16. You Try; • A sample of 1500 dogs finds that only 1037 of them are “altered”. Find a 99% confidence interval for the population proportion of altered dogs.

  17. Possibilities; Is it possible that our confidence interval does not contain the population proportion? Oh yes, and this will happen 5% of the time with a 95% confidence interval.

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