7.3 notes

Sampling Distributions

• Sampling distribution: a distribution of many samples from a population
• The center of the sampling distribution is at the center of the population
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• There’s a formula to find the standard deviation of the sampling distribution of sample proportions (p̂s), which works as long as P>10n
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• The sampling distribution is approximately normal if np > 10 and n(1-p) > 10
  • If this is true, we can use the two equations above to calculate z-scores

Proportions vs. Means

• Proportions are generally associated with categorical variables

• Means are generally associated with quantitative variables

  

• Generally, if an SRS of size n is drawn from a normal population, then the sampling distribution of x̄ will be approximately normal

Central Limit Theorem

• Generally, if an SRS of size n is drawn from any population with parameters µ and σ
  • When n is large, the sampling distribution of x̄ is
  • The generally accepted value for “large” is n≥30