Statistical Inference Hypothesis Testing Sampling Distributions: is normally distributed with mean: and standard deviation: Sample Mean: X If the is not known, we use the unbiased estimates when we find the estimated value of. Confidence Interval Estimation Mean ( Known Proportion ( ) Unknown Z s t, p p p) n Required Sample Size (In Both Cases, always Round UP): Z 2 2 Mean: where E is the error of the estimation or sampling error E2 Z 2 ( ) Proportion: 2 2 where E is the margin of error E 6. Price Indexes Simple Weighted Index: I Pt 100 P0 Unweighted Aggregate Price Index: I Pt 100 P0 Pt Q0 P0 Pt Qt 100 Paasche Price Index: I P0 Laspeyres Price Index: I 5. P(A P ( A ) P( ) P( B) P( B) P( A) if A and B are independent Conditional Probability: P ( Statistical Independence: A and B are independent, if and only if P ( A) Multiplication Rule: P ( A B ( B ) P ( ( A ) P A) P ( A ) P (B) if A and B are independent Bayes Theorem: P ( A P(A P P(B) P (A ) P( P( ) (B ) 3. Addition Law: P ( A B ) ( A P ( B ( A B ) P ( A ) P ( B ) if A and B are mutually exclusive. Probability Theory If N is the total number of opportunities for the event to occur and x is the time of events the event A has occurred: P ( A x N Marginal Probability: P ( A ( A P(A ) where B and are mutually exclusive and collectively exhaustive events. s Coefficient of Variation: CV 100 or CV Standardized Value or and for a given X Empirical Rule: The interval of values one standard deviation either above or below the mean, 1, contains approximately of the items or people within the sample. Rule 3: If the result is neither an integer nor fractional half, round the result to the nearest integer and select the ranked value. Rule 2: If the result is a fractional half, then the quartile is equal to the mean of the corresponding values. Quartiles: 4 Second Quartile Position: 2 3 ( ) Third Quartile Position: 4 First Quartile Position: Quartile Rules: Rule 1: If the result is an integer, then the quartile is equal to the ranked value. Descriptive Statistics Sample Mean: xi n Population Mean: xi Sample Variance: N ( x )2 x2i 2 Population Variance: ( xi )2 x 2i N N The standard deviation is the positive square root of the variance. Related Studylists Bstats probability + Statistical Reasoning Business Statistics Preview text Formula Sheet 1.
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