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24 Cards in this Set
- Front
- Back
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Test Statistic (Small sample) |
Y = # of successes |
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Test Statistic (Large Sample) |
Z = (# of successes - np) / SQRT(np(n-p)) |
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Another form of Z |
P-hat - P / P(1 - P) / n) |
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Confidence interval for Proportion |
P-hat +/- z * SQRT(P-hat(1-P) / n) |
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Normal distribution formula for z |
(x-m) / sigma |
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Null Distribution for small proportion sample |
Y ~ Bin (n,p) |
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Null Distribution for large proportion sample |
Z ~ N(0,1) |
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Rules for using t distribution |
1. Assume that you are sampling from a normal population (Histogram should be roughly bell shaped) 2. Sigma is unknown and estimated with s |
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Null distribution for t |
Tn-1 (degrees of freedom) |
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Type 1 Error |
Rejecting a true null hypothesis |
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Type 2 Error |
Failing to reject a false null hypothesis |
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What should your alpha level be if you think a Type 1 error is worse? |
.01 |
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What should your alpha level be if you think a Type 2 error is worse? |
.1 |
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What should your alpha level be if both errors are equal? |
.05 |
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Test statistic for small sample mean problem using t |
t = (X-bar - M)/s/SQRT(n) |
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Confidence interval for small sample mean problem using t |
M: X-bar +/- t * (s/SQRT(n)) |
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Test Statistic for large mean problem using Z |
Z = (X-bar - M)/s/SQRT(n) |
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Confidence Interval for large mean problem using Z |
X +/- Z * (s/SQRT(n)) |
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Test Statistic for two mean problem |
Z = [(X-bar1 - X-bar2) - (M1-M2)]/[Sp * SQRT(1/n1+1/n2)] |
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Pooled Standard Deviation Formula (Sp) |
Sp = SQRT[(n1-1)/(n1+n2-2) * S1^2 + (n2-1)/(n1+n2-2) * s2^2) |
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Confidence interval for two mean problem |
(X-bar1-X-bar2) +/- t or z * Sp *SQRT(1/n1 +1/n2) |
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B1-hat formula |
Y-bar - B1-hat*X-bar |
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Bo-hat formula |
r * (sy/sx) |
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Confidence interval for slope |
B1-hat +/- t or z * standard error |
