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Unformatted text preview: 2 of 13 1.1 Introduction POINT ESTIMATES Notation p population proportion. Note: proportion, percentage, and probability can all be consid- ered as p . p estimate of sample proportion with x successes in n trials. p = x n , q = 1- p (1) point estimate. Definition 1.1 A single value (or point) used to approximate a population parameter. The sample proportion p is the best point estimate of the popula- tion proportion p . Importance of proper sampling. If a sample is not representative of the population, p will not be a useful estimate of p . Use proper sampling techniques! Example 2 . Point estimate of proportion of people who wear corrective lenses in the US using class data: R: x = sum( corrective lenses == YES) R: x [ 1 ] 10 R: n = length ( corrective lenses ) R: n [ 1 ] 18 R: p . hat = x/n R: p . hat [ 1 ] 0.55556 Question 1 . How good is the estimate of p ? How precise is the estimate? Question 2 . What do we need to know about p to determine the precision of the estimate? Anthony Tanbakuchi MAT167 Estimating a population proportion 3 of 13 1.2 Confidence intervals Confidence interval. Definition 1.2 is a range of values an interval used to estimate the true value of a population parameter. It provides information about the inherent sampling error of the estimate. (In contrast to point estimate.) Just as we used the empirical rule to estimate an interval 95% of the data would fall within if the datas distribution was normal, we can construct a similar interval for a statistic given its sampling distribution ....
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