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Confidence intervals for proportions. Sec 9.3. The Plan; For building a 95% confidence interval. The Plan; For building a 95% confidence interval. What do we use for (se). What to use for Standard Error,. The standard error for a sampling distribution of proportions is normally;

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## Confidence intervals for proportions

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**The Plan;For building a 95% confidence interval**What do we use for (se)**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.**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**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**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**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**Lets try;**73.5% Step Two: We need to find the standard error in order to build our intervals.**Lets try;**73.5% Step Two: We need to find the standard error in order to build our intervals.**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%**Lets try;**73.5% Therefore we are 95% confident that between 61% and 79% of Americans will be having cranberries with their Thanksgiving meal.**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.**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**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.**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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