5% with a standard error of 3. We take a random sample of 50 households in order to estimate the percentage of all homes in the United States that have a refrigerator. In an unbiased random surveysample proportion = population proportion + random error. 1. We know that estimates arising from surveys like that are random quantities that vary from sample-to-sample. 4 below).

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Table 9. A random sample is gathered to estimate the percentage of American adults who believe that parents should be required to vaccinate their children for diseases like measles, mumps, and rubella. Commonly Used MultipliersTo interpret a confidence interval remember that the sample information is random – but there is a pattern to its behavior if we look at all possible samples. 3 and 9. The margin-of-error being satisfied means that the interval includes the true population value.

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Creative Commons Attribution NonCommercial License 4. It turns out that 49 of the 50 homes in our sample have a refrigerator. What is the population value being estimated by this sample percentage? What is the standard error of the corresponding sample proportion?Recap: the estimated percent of Centre Country households useful source don’t meet the EPA guidelines is 63. We call this estimate the standard error of the sample proportionStandard Error of Sample Proportion = estimated standard deviation of the sample proportion =\[\sqrt{\frac{\text{sample proportion}(1-\text{sample proportion})}{n}}\]The EPA considers indoor radon levels above 4 picocuries per liter (pCi/L) of air to be high enough to warrant amelioration efforts.

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Can we use the formulas above original site make a confidence interval in this situation?Except where otherwise noted, content on this site is licensed under a CC BY-NC 4. The Normal approximation tells us thatThus, a 68% confidence interval for the percent of all Centre Country households that don’t meet the EPA guidelines is given byA 95% confidence interval for the percent of all Centre Country households that don’t meet the EPA guidelines is given byFor large random samples a confidence interval for a population proportion is given by\[\text{sample proportion} \pm z* \sqrt{\frac{\text{sample proportion}(1-\text{sample proportion})}{n}}\]where z* is a multiplier number that comes form the normal curve and determines the level of confidence (see Table 9. 0

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Start Over . Tests in a sample of 200 Centre County Pennsylvania homes found 127 (63.

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When we do probability calculations we know the value of p so we can just plug that in to get the standard deviation. 5%) of these sampled households to have indoor radon levels above 4 pCi/L. However, we can get a very good approximation by plugging in the sample proportion. Each possible sample gives us a different sample proportion and a different interval. 4%.

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1 for some common multiplier numbers). The fact that random errors follow the normal curve also holds for many other summaries like sample averages or differences between two sample proportions or averages – you just need a different formula for the standard deviation in each case (see sections 9. But when the population value is unknown, we won’t know the standard deviation exactly. The Normal Approximation tells us that the distribution of these random errors over all possible samples follows the go curve with a standard deviation of\[\sqrt{\frac{\text{population proportion}(1-\text{population proportion})}{n}} =\sqrt{\frac{p(1−p)}{n}}\]The random error is just how much the sample estimate differs from the true population value.

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0 license. Notice how the formula for the standard deviation of the sample proportion depends on the true population proportion p. In Lesson 8we learned what probability has to say about how close a sample proportion will be to the true population proportion. But, even though the results vary from sample-to-sample, we are “confident” because the margin-of-error my review here be satisfied for 95% of all samples (with z*=2). .

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