T1. Location/Spread/Shape/Outlier: egX_bar, variance s^2, sds (and p=X/n to estimate Π) using our calculator
T2. 95% or 99% CI for pop mean (and pop proportion)
2.1 sigma=given: alpha=0.05 or 0.01=1%
[X_bar - 1.96 * sigma/n^0.5, X_bar + 1.96 * sigma/n^0.5] plus comments 2.2 sigma=not given, use s instead, alpha=0.05
[X_bar - tc * s/n^0.5, X_bar + tc * s/n^0.5]
wheretc=tc(0.025,9)=2.262 for 95% CI and a sample of n=10
T3. Box-plot, histogram, s^2 comments
T4. Basic probability P(X=3) or pi should be in between 0 and 1 inclusive, and the sum of prob's = 1
E(X)=? Var(X)=? SD(X)=Var(X)^0.5
T5. Binomial Probability X~B(n, p)
with n=5, p=0.2 for selecting a girl, q=0.8 for selecting a boy
5.1 Probability for exactk=3 girls in the sample of 5 students
Let X be the number of girls selected in the sample of 5
P(X=3)=0.0512 using the table method
5.2 Probability for at most 2 girls in the sample of 5 students
P(X< or = 2) = P(X=0) + P(X=1) + P(X=2) =
5.3 Probability for at least 2 girls in the sample of 5 students
P(X> or = 2) = P(X=2) + P(X=3) + P(X=4) + P(X=5) =
T6. Poisson Probability, using Poisson table
6.1 Probability for exact X=3,
6.2at most X< or =3,
6.3 at least X > or =2
T7. Normal Probability X ~ N(μ, σ2)
7.1 Probability for exact P(X=3) = 0
7.2 at most 3, or less than 3, P(X < or = 3)
7.3 at least 2, or more than 2, P(X > or =2)
7.4 find X=a for eg top 10% or low 20%
7.5 probabilities involving X_bar: X_bar ~ N(μ, σ2) with σ/n0.5
T8. Hypos Tests: which test to use? H0=? 1- or 2-tailed for H1, p_value<α ?com/dec/comments
one sample tests: z-test for σ given, t-test for σ not given two sample tests: t-paired, t-ind-equ-var, t-ind-unequ-var
T9. Regression
9.1 Scatter plot for y vs x:
positive/neg, liner/not, strong/weak, outliers/not
9.2 Residual plot for res vs x, or res vsy_hat, or res vs index:
random/not, equlvar/not, depend/not, outlier/not
9.3 Tables/Numbers calculations/comments: R^2=SSR/SST, 0< R^2<1