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Stats 141 Formula Sheet.docx

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University of Alberta
Oksana Kotovych

Sampling Distribution of a Sample Mean Sampling Distribution of a Sample Proportion #ofsuccesse sin sample O P = q = 1-p E(y) = u(y) = u SD(y) = Ơ(y) = n Assumptions: n #ofsuccesse sin population -np>10 and nq>10 Assumptions: P = q = 1-p #ofobservationsin population -sample values independent -sample values independent of each other -random sample -n reasonably large (>30) or pop. Normal pq E(p) = u(p) = p SD(p) = O(p) = -n no larger than 10% of pop. -random sample n -n no more than 10% of population observationmean p u(p) Z = = SD o(p) Confidence Intervals for Proportions Assumptions: Hypothesis Testing for Proporions: P O hypothesized value q = 1OP O Estimated SD = SE(p) = pq -independence n -random sample H O P=P o HA: P>, -np>10 and nq>10 np >10 n Type I Error – Reject Howhen H io true o Eg. 95% of samples this size will produce CI’s that capture p. Type II Error – Fail to reject when o is false nq o10  Z  ME n Choosing Sample Size: n =  pq Obtaining CI given ME: Z = ME  pq Goodness of Fit Test: Comparing Counts ( χ ²): Right Skewed H o Pk=(P o k H A H os false Expected Count = (total # of observations)(hypothesized value for that category) χ ²>0 χ ² = ∑all cellsserved exp ected  = ∑all cells E) df=k-1 Notation: exp ectedcount E K=number of categories Assumptions: P1=true proportion for category 1 -data coun
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