Biostatistics, Chapter V & VI Notes

Sampling Distributions

• Basic properties of the sample mean ȳ
  • Identical to population mean μ
  • Variance of a sample mean σ^2 / n. The standard deviation of the sample mean is the population standard dev (σ) divided by sqrt(n). It’s called the standard error of the mean
  • As a sample size increases, the standard error of the mean decreases
• σȳ = σ/sqrt(n)
• Z = (Ȳ - μ) / (σ * 1/sqrt(n))
• Central Limit Theorem: all random samples of the same size n (when large enough), the distribution of Z is approx. normal with mean 0 and variance 1.
• Note: when something asks for the probability of “at most two” sum the probabilities for 0, 1, and 2
• To flip (Z < -#), it becomes (Z > #)
• Two types of statistical inference: estimation, hypothesis testing
• T distribution has the same general shape as the normal distriution
  • The sample size must be greater than or equal to 25 to do the t distribution without the normal assumption
• The standard deviation is greater than one, increases when sample size decreases
• Alpha = 1 - (confidence) divided by 2
• T sub alpha, n-1
• S is the same as sigma
• Plus or minus the average mean with the tscore times S/sqrt(n) for the distribution
• This tscore times S/sqrt(n) is the margin of error
• The degree of freedom for a normal distribution is infinity

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