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When calculating the confidence interval for finite sample population, there are several factors that are taken into consideration. The first is the point estimate which is the number of estimates of the value of the population parameter. The population parameter on the other hand is the descriptive measure of our population. At this point it is important to use symbols to denote the population and the sample population differently.
We find that when the sample size and the sample proportion remain the same in size (Moore, McCabe and Craig, 2009). The confidence interval for this population will be narrower than the confidence interval of the population. However, when we have a confidence level and the proportion of the population remaining the same, the confidence interval of the population proportion will be wider that that of the sample population. Therefore statistically the confidence level and the sample size remain the same, when the confidence interval of the population proportion is wider when is larger than when it’s smaller.
In statistics when the confidence interval of the population is given we can calculate the sample size. This is obtained using the formula for n, (Stevens, 2009).
It is noted that B represents the value that is farthest from the population that allows the sample mean to be. n is the size of the sample that is required and p represents the population proportion.
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