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Final

# Stats 141 Formula Sheet.docx

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University of Alberta

Statistics

STAT141

Oksana Kotovych

Fall

Description

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 observationmean 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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