week 7 - statistical inference

statistic vs parameter

→ use statistics to estimate parameters

• statistic: characteristics of a sample (population)

  • can change

• parameter: characteristics of a population

  • describes the actual population

  • fixed value (whole population)

→ example:

sampling distribution and standard error

• standard error: measures how much the sample statistic varies from sample to sample (smaller than the STD for the population)

• population VS the sample:

  

• example:

  

• large numbers:

  When n is large enough:

  • the shape of the sampling distribution of the sample mean is approximately norma —- regardless of the original distribution

  • the sample mean more closely approximates the
    population mean

• increase sample size = mean decreases (error)

  → ex: n is increasing from 5 to 30 = error is decreasing

central limit theorem

• If you have a population with mean μ and standard deviation σ and take large random samples from the population with replacement

  • the distribution of the sample means will be approximately normally distributed

• we can calculate a Z-score (using STD error in the denominator)

notation