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In this section we consider confidence intervals where the number of sample members is not a negligible proportion of the number of population members. Generally, the sample size is considered to be relatively large compared to the population size if it is more than 5% of the population size, that is, if > 0.05N. We assume that the sample is sufficiently large and that recourse to the central limit theorem is appropriate. As a result, the finite population correction (fpc) factor, (N - 7/(N - 1), which was introduced in Chapter 6, will be used. In these situations the individual members are not distributed independently of one another and sampling is without replacement, Population Mean and Population Total Here, we consider problems where a sample of a individuals or objects is to be drawn from a population containing N members. We develop confidence intervals for the population mean and the population total when the sample size is more than 5% of the population size. 289 7.6 Confidence interval Estimation: Finite Populations k2 Estimation of the Population Mean, Simple Random Sample, Finite Population Letxe XX, denote the values observed from a simple random sample of size n, taken from a population of N members with mean 4. 1. The sample mean is an unbiased estimator of the population mean, . The point estimate is 2. An unbiased estimation procedure for the variance of the sample mean yields the point estimate (7.11) 3. A 10001 - 0)% confidence interval for the population mean is given by I ! - (7:12) where ME, the margin of error, is given by ME = 1 (7.13) xample Mortgages (Confidence Interval) In a particular city 1,118 mortgages were financed last year. A random sample of 60 of these had a mean amount $87,300 and standard deviation $19,200. Estimate the mean amount of all mortgages financed in this city last year, and find a 95% confidence interval