FobelloE

2021-03-11

1) Describe sampling distributions and sampling variavility
2) Explain The Central Limit Theorem
3) Explain how confidence intervals are created and what can they tell us about population parameters

Leonard Stokes

Step 1
1)
The term "sampling distributions" describes the probability distributions of all potential values for a sample statistic, such as the sample mean.
The sampling variability reveals the variations in an estimate across various samples. It is frequently calculated using the variance or standard deviation. Three elements contribute to variability,
The size of the population
The size of the sample
The sampling method (with or without replacement)
Step 2
2)
The central limit theorem tells us that in a random sample of size n taken from a population, its sampling distribution can be approximated to a normal distribution by taking a larger sample size. That is, whatever might be the population distribution, the sampling distribution of a sample statistic can be approximated to normal by increasing the sample size.
Step 3
3)
The confidence interval are created using the sample statistic and the margin of error.
$CI=\stackrel{―}{x}±{Z}_{\frac{\alpha }{2}}\left(\frac{\sigma }{\sqrt{n}}n\right)$
$=\stackrel{―}{x}±ME$
${Z}_{\frac{\alpha }{2}}$ represents the critical value of the normal distribution and this distribution is used if the population standard deviation is known. For unknown population standard deviation, the sample standard deviation is used with student’s t distribution.
The constructed confidence interval with say 95 or 90 percent confidence level tells us that if repeated samples were to be taken and confidence intervals were to be built, then 95 or 90 percent of these constructed confidence intervals would contain the true value of the parameter (mean).

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