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Chapter 6 Notes.docx

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Biology 2244A/B
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Bio 2244B Textbook Notes Chapter 6 61 62 63 64March th13 201261 OverviewDefinitionsThe two major applications of inferential statistics involve the use of sample data to 1Estimate the value of a population parameter2Test some claim or hypothesis about a population62 Estimating a Population ProportionThis section only considers cases in which the normal distribution can be used to approximate the sampling distribution of sampling proportionsRequirements for using a normal distribution as an approximation to a binomial distribution1The sample is a simple random sample SRS2The conditions for the binomial distribution are satisfied ie there is a fixed number of trials the trials are independent there are 2 categories of outcomes and the propbabilities remain constant for each trial3The normal distribution can be used to approximate the distribution of sample proportions because np5 and nq5We know that different samples naturally produce different results but this section assumes that those sample differences are due to chance random fluctuations not some unsound method of samplingNotation for proportionspproportion of successes in the entire populationxp sample proportion of x successes in a sample of size n nq1 psample proportion of failures in a sample of size n If we want to estimate a population proportion with a single value the best estimate is p Because p consists of a single value it is called a point estimatePoint estimate a single value or point used to approximate a population parameterThe sample proportion p is the best estimate of the population proportion pWe use p as the point estimate of p because it is unbiased and is the most consistent of the estimators that could be usedoIt is unbiased in the sense that the distribution of sample proportions tends to center about the value of p that is sample proportions p do not systematically tend to underestimate p nor do they systematically tend to overestimate pThe point estimate has the serious flaw of not revealing anything about how good it is thus we have developed another type of estimate that consists of a range or an interval of values instead of just a single valueConfidence interval interval estimate a range or interval of values used to estimate the true value of a population parameterA confidence interval is associated with a confidence level which gives us the success rate of the procedure used to construct the confidence interval oThe confidence level is often expressed as the probability or area 1aoThe value of a is the complement of the confidence level so for a 095 95 confidence level a005Confidence level the probability 1a often expressed as the equivalent percentage value that is the proportion of times that the confidence interval actually does contain the population parameter assuming that the estimation process is repeated a large number of times The critical value z is the positive z value that is at the vertical boundary separating an area 2aof a2 in the right tail of the standard normal distribution
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