1. To calculate z-score
    Image Upload 2
  2. Fromale for z-score to data value
    X = µ + (zσ)
  3. 3 types of probability
    • subjective (personal judgement)
    • Analytic/Theoretical - study all possible outcomes
    • Expected relative frequency (Empirical) - on the long run, average
  4. The Addition Rule
    • given mutually exclusive events, sum the probabilities
    • keyword: OR
  5. Multiplication Rule
    • for joint probabilities
    • keyword: AND
  6. Chi Square Goodness of Fit
    • Used to test frequency distributions for ONE dimension
    • Ei= npi || df = (k-1)
    • Image Upload 4
  7. Chi Square: Contingency
    • Er,c = (sum of Row) x (sum of column)
    • sample size

    df = (r-1)(c-1)
  8. When do we reject the null?
    x2(observed) > x2(critical), reject the null
  9. Sampling Error
    Random variability btwn observations or statistics due to chance
  10. Sampling distribution
    The distribution of a statistic over repeated sampling from a specified population
  11. properties of Sample Means
    • the mean of the sample is equal to the population mean (no calculation)
    • the standard deviation of the sample is (standard error of the mean)
    • Image Upload 6
  12. Variance formula
    Image Upload 8
  13. The Null Hypothesis
    • The hypothesis that the manipulation had no effect.
    • always contains = or ≤ or ≥
  14. The alternative hypothesis
    always contains ≠, < or >
  15. The critical values
    • represent the point at which we reject the null
    • we reject the null when we exceed the critical value
  16. 2 types of hypothesis tests
    One tailed: one direction for rejection; left or right tailed

    2 tailed: rejects null when value is too extreme in either direction; non directional
  17. Decision based on a p-value
    If p ≤ α (in critical region), reject the null

    If p ≥ α (not in critical region), fail to reject the null
  18. Types of errors
    Type I error occurs if the null hypothesis is rejected but it's actually true (most serious)

    Type II error occurs when the null hypothesis is not rejected but it's actually false
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