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Sample Size and Population Mean

Q1: Why does the sample size play such an important role in reducing the standard error of the mean? What are the implications of increasing the sample size?

Q2: Why might one be interested in determining a sample size before a study is undertaken? How do population variability and a level of certainty affect the size of the sample needed in a study?

Q3: How do estimation procedures differ for the population mean when the population standard deviation is known or unknown? What does a 95% confidence level actually mean in terms of probabilities?

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Answers to Sample Size and Population Mean are provided, with detailed explanations.