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Chapter Twelve

Chapter Twelve. Sampling: Final and Initial Sample Size Determination. Symbols for Population and Sample Variables. _. _. _. _. _. Sample vs. Population. Population parameters are unknown Sample statistics are used as estimates of parameters Population parameters are fixed

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Chapter Twelve

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  1. Chapter Twelve Sampling:Final and Initial SampleSize Determination

  2. Symbols for Population and Sample Variables _ _ _ _ _

  3. 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).

  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 Correspondingto Known Values Area is 0.3413 Z Scale

  6. 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 + 1.96 z values. The 95% confidence interval is given by + 1.96 = 182.00 + 1.96(3.18) = 182.00 + 6.23 Thus the 95% confidence interval ranges from $175.77 to $188.23. The probability of finding the true population mean to be within $175.77 and $188.23 is 95%.

  7. Sample Size Determination for Means and Proportions _ -

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