Presentation on theme: "Sampling: Final and Initial Sample Size Determination"— Presentation transcript:
1 Sampling: Final and Initial Sample Size Determination Chapter TwelveSampling: Final and Initial Sample Size Determination
2 Symbols for Population and Sample Variables _____
3 Sample vs. Population Population parameters are unknown Sample statistics are used as estimates of parametersPopulation parameters are fixedSample statistics change from sample to sampleIf 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).
4 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.
5 Finding Probabilities Corresponding to Known Values Area isZ Scale
6 The Confidence Interval Approach Note that is estimated by . The confidence interval is given byWe 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%.
7 Sample Size Determination for Means and Proportions _-