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**Sampling: Final and Initial Sample Size Determination**

Chapter Twelve Sampling: Final and Initial Sample Size Determination

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**Symbols for Population and Sample Variables**

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**Sample vs. Population Population parameters are unknown**

Sample statistics are used as estimates of parameters Population parameters are fixed Sample statistics change from sample to sample If simple random samples of size n are drawn from a population with mean µ and variance 2, then when n is large, the sample mean will be approximately normally distributed with mean equal to µ and variance equal to 2/n (known as standard error of the mean).

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**Definitions and Symbols**

Standard error of the estimate: Standard deviation of the parameter to be estimated in the research. Precision level: When estimating a population parameter by using a sample statistic, the precision level is the desired size of the estimating interval. This is the maximum permissible difference between the sample statistic and the population parameter. Confidence level: The confidence level is the desired probability that a confidence interval will include the population parameter.

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**Finding Probabilities Corresponding to Known Values**

Area is Z Scale

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**The Confidence Interval Approach**

Note that is estimated by . The confidence interval is given by We can now set a 95% confidence interval around the sample mean of $182. As a first step, we compute the standard error of the mean: From Table 2 in the Appendix of Statistical Tables, it can be seen that the central 95% of the normal distribution lies within z values. The 95% confidence interval is given by + 1.96 = (3.18) = Thus the 95% confidence interval ranges from $ to $ The probability of finding the true population mean to be within $ and $ is 95%.

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**Sample Size Determination for Means and Proportions**

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