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118 Cards in this Set
- Front
- Back
Population
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Entire group of people to be studied
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Sample
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Subset of population that is being studied
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Statistic
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Numerical summary of sample
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Parameter
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Numerical summary of population
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Qualitative data
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Non-numeric or numeric but cannot perform arithmetic operations
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Quantitative data
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Numbers, can perform arithmetic operations with meaning
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Discrete data
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"Number of," can be counted
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Continuous data
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No space between; measurements
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Random
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Every outcome has an equally likely chance of ocurring
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Relative frequency
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Part / whole
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Pie chart
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Multiply relative frequency by 360 to get degrees
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Lower class limit
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Smallest value
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Upper class limit
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Highest value
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Class width
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Subtract consecutive lower class limits
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Range
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Maximum - minimum
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Variance
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(X1 - μ)^2
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Z score
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(x - μ) / σ
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IQR
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Q3 - Q1
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Lower fence
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Q1 - 1.5(IQR)
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Upper fence
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Q3 + 1.5(IQR)
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Probability
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Measure of chance behavior
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Experiment
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Anything done with an unknown outcome
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Sample space
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All possible outcomes
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Event
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Collection of outcomes
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Empirical probability
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Comes from data, equals relative frequency
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Classical method
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Treat everything equally as likely
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Subjective probability
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Probability obtained from personal judgement
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Disjoint / mutually exclusive
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2 events with no outcomes in common
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Addition rule for disjoint
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P(A or B) = P(A) + P(B)
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Addition rule if not disjoint
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P(A or B) = P(A) + P(B) - P(A & B)
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Complement (E^c)
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All outcomes in sample space s that are not outcomes of event E. P(E^c) = 1 - P(E)
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Independent events
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Events whose occurrence do not affect each other
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Multiplication rule for independent
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P(A and B) = P(A) * P(B)
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Multiplication rule for dependent
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P(A and B) = P(A) * P(B|A)
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Conditional probability for independent
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P(B|A) = P(A & B) / P(A)
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Conditional probability for dependent
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P(E & F) = P(F)P(F|E)
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0!
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1
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1!
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1
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Permutation
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nPr = n!/(n-r)!
Order is important |
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Combination
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nCr = n!/r!(n-r)!
Order is not important |
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Mean - discrete random variables
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μ = Σ[x*P(x)]
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Criteria for binomial probability experiment
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Performed fixed number of times, trials are independent, 2 mutually exclusive outcomes, probability of success is the same for each trial
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Binomial probability distribution
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Binompdf(n,p,x)
For "x = ..." |
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Binomial cumulative distribution
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Binomcdf(n,p,x)
For "x < ..." or "x ≤ ..." or "x > ..." or "x ≥ ..." |
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Mean - binomial
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μ = n*p
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Standard deviation - binomial
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σ = √(npq)
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Normal probability distribution
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μ = 0, σ = 1
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Area for standard normal variables
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Normalcdf(lower bound, upper bound, μ, σ)
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Critical value
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Invnorm(area to left)
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Sample proportion
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P-hat = x/n
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90% confidence - critical value
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1.645
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95% confidence - critical value
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1.96
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99% confidence - critical value
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2.575
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Sample size (T)
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n = ([Zα/2 * σ]/E)^2
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E (Z interval)
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E = Zα/2*√[P(1-p)/n]
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Sample size (Z) [with prior estimates]
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N = p(1-p){[(Zα/2)/E]}^2
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Sample size (Z) [no prior estimates]
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N = .25{[Zα/2]/E}^2
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Χ^2 distribution
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X^2 = [(n-1)s^2]/σ^2
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Unusual event
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P(x<0.05)
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Standard normal distribution
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μ=0, σ=1
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Finding percentiles
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Invnorm(percentage in decimal form, μ, σ)
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Finding area to left (standard normal dist.)
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Normalcdf(-∞, z, μ, σ)
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Finding area to right (standard normal dist.)
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Normacdf(z, ∞, μ, σ)
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Finding area between 2 z-scores
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Normalcdf(z1, z2, μ, σ)
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Finding area - P(x=...)
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Binompdf(n, p, x)
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Finding area - P(x≥...)
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Binomcdf(n, p, [x-1])
1 - ans |
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Finding area - P(x≤...)
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Binomcdf(n, p, x)
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Finding area - P(x<...)
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Binomcdf(n, p, [x-1])
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Confidence interval - X^2
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√{[(n-1)s^2]/X^2*1-α/2} < σ^2 < √{[(n-1)s^2]/X^2*1-α/2}
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Hypothesis testing - mean
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Use t-distribution
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Hypothesis testing - population
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Use z-distribution
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Hypothesis testing - standard deviation
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Use X^2 distribution
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Check for outliers - mean
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Box plot
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Check for outliers - p & z
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np(1-p)≥10
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P(TI)
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α
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P(not TI)
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1-α
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P(Type II)
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β
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P(not Type II)
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1-β
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Test statistic in critical region
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Reject hypothesis
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Test statistic not in critical region
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Don't reject hypothesis
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Don't reject hypothesis
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There is not sufficient evidence...
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Reject hypothesis
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There is sufficient evidence...
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Confidence interval - μ - σ known
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Use z-interval
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Confidence interval - μ - σ unknown
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Use t-interval
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Confidence interval - p
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Use 1-prop-Z-interval
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Confidence interval - σ
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Use X^2
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Hypothesis test - μ
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Use t-test
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Hypothesis test - p
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Use 1-prop-z-test
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Hypothesis test - σ
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Use X^2
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Dependent hypothesis test
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L1-L2 > L3
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Dependent hypothesis test - null hypothesis
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H0: μ1=0
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Dependent hypothesis test/interval
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Use t-test & t-interval
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Independent hypothesis test - null hypothesis
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H0: μ1 = μ2
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Independent hypothesis test - test/interval
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2-samp-t-test & 2-samp-t-interval
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2 population proportions - null hypothesis
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H0: p1 = p2
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2 population proportions - test/interval
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Use 2-prop-z-test & 2-prop-z-interval
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Sample size - 2 population proportions [with prior estimates]
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n = [p1(1-p1)+p2(1-p2)][(Zα/2)/E]^2
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Sample size - 2 population proportions [no prior estimates]
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n = .25[(Zα/2)/E]^2
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Predictor/explanatory variable
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X
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Response variable
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Y
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To find r (correlation coefficient)
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(L1 - x-bar)/Sx > L3
(L2 - y-bar)/Sy > L4 (L3 + L4) > L5 Linreg(ax+b) |
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R close to 1
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Strong positive correlation
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R close to -1
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Strong negative correlation
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R close to 0
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Weak correlation
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Residual
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Observed - predicted
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Equation of Least-squares regression line
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Y-hat = b1x + b0
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B1 (least-squares regression line)
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r * (Sy/Sx)
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B0 (least-squares regression line)
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Y-bar - b1*x-bar
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Sum of square residuals
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Sum of (y - y-hat)^2
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Pareto chart
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Bar chart drawn in decreasing order of frequency or relative frequency
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Bar chart/graph
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Bars do not touch
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Histogram
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Bars touch
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Graph interpretation - μ & median at same line
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Symmetric
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Graph interpretation - μ to left of median
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Skewed left
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Graph interpretation - μ to right of median
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Skewed right
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Relative frequencies/probabilities must add to equal...
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1
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Confidence interval for a parameter
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An interval of numbers combined with the likelihood the interval contains the unknown parameter
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Margin of error for confidence interval with known σ
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±Zα/2 * (σ/√n)
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