Which of the following tasks can be performed by a researcher who understands the basics of the central limit theorem (CLT)?
Drawing representative samples from any target populationObtaining sample statistics from a random sample that work as accurate estimates of the target population’s parameters
A researcher who understands the basics of the central limit theorem can perform the following tasks:
1. Estimation of population parameters: CLT allows the use of sample means to estimate population means and other parameters with greater accuracy and reliability. A researcher can use this property to estimate various population parameters such as the mean, variance, and standard deviation.
2. Hypothesis testing: CLT allows the use of sample means to conduct hypothesis testing. A researcher can use this property to test hypotheses about the population mean or other parameters.
3. Confidence intervals: CLT allows us to estimate confidence intervals, which are interval estimates for population parameters based on sample statistics. A researcher can use this property to estimate the range in which the population parameters may lie.
4. Sample size determination: CLT is useful in determining the appropriate sample size for a particular study. A researcher can use this property to determine the minimum sample size required to achieve a specific level of precision for the estimates or test of significance.
Overall, understanding the central limit theorem enables researchers to use statistical techniques that rely on the assumptions of the theorem, to make statistical inference about the population parameters.
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