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Fromale for zscore to data value
X = µ + (zσ)

3 types of probability
 subjective (personal judgement)
 Analytic/Theoretical  study all possible outcomes
 Expected relative frequency (Empirical)  on the long run, average

The Addition Rule
 given mutually exclusive events, sum the probabilities
 keyword: OR

Multiplication Rule
 for joint probabilities
 keyword: AND

Chi Square Goodness of Fit
 Used to test frequency distributions for ONE dimension
 E_{i}= np_{i } df = (k1)

Chi Square: Contingency
 E_{r,c }= (sum of Row) x (sum of column)
 sample size
df = (r1)(c1)

When do we reject the null?
x^{2}(observed) > x^{2}(critical), reject the null

Sampling Error
Random variability btwn observations or statistics due to chance

Sampling distribution
The distribution of a statistic over repeated sampling from a specified population

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)


The Null Hypothesis
 The hypothesis that the manipulation had no effect.
 always contains = or ≤ or ≥

The alternative hypothesis
always contains ≠, < or >

The critical values
 represent the point at which we reject the null
 we reject the null when we exceed the critical value

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

Decision based on a pvalue
If p ≤ α (in critical region), reject the null
If p ≥ α (not in critical region), fail to reject the null

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

