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
    *
• There’s a formula to find the standard deviation of the sampling distribution of sample proportions (p̂s), which works as long as P>10n
    *
• 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