7 Estimates and sample sizes - Lecture#7 Chapter 7...

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Lecture #7 Chapter 7: Estimates and sample sizes In this chapter, we will learn an important technique of statistical inference to use sample statistics to estimate the value of an unknown population parameter. 7-2 Estimating a population proportion Recall: A point estimate is a single value estimate for a population parameter. The most unbiased point estimate of the population proportion is the sample proportion, . An interval estimate (confidence interval) is an interval, or range of values, used to estimate a population parameter. For example 0.476<p<0.544 The level of confidence (1- ) is the probability that the interval estimate contains the population parameter. For example, we are 90% confident that the above interval contains the true value of p. “We are 90% confident” means that if we were to select many different samples of size n and construct the confidence interval, 90% of them actually contain the value of the population proportion p. We know from the central limit theorem that when n>30, the sampling distribution of sample proportion is a normal distribution. The level of confidence ( 1- is the area under the standard normal curve between the critical values - and . Critical values are values that separate sample statistics that are probable from sample statistics that are improbable, or unusual. ( 1- is the percent of the area under the normal curve between - and . For example, if ( 1- , then and =0.05. 5% of the area lies to the left of =-1.645 and 5% lies to the right of =1.645. Example 1: Find the critical value corresponding to the given degree of confidence. a) 99% b) 97%
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The margin of error , denoted by E , is the greatest possible distance between the observed sample proportion and the true value of the population proportion p. = Thus a ( 1- confidence interval for the population proportion is E <p < +E. Round-off rule for confidence interval estimate of p: Round the confidence interval limits for p to 3 significant digits.
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