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Probs & Stats 2
probability and statistics concepts
| Question | Answer |
|---|---|
| Discrete | Finite number |
| Continuous | Infinite without gaps |
| Nominal | Categories No order |
| Ordinal | Ordered but difference between is meaningless Relative comparison Ex:grades |
| Interval | Ordered but meaningful Does not start at 0 Ex:temp |
| Ratio | Ordered/meaningful Starts at 0 Ex:distance |
| Systematic sample | Start point Select every Kth element |
| Convenience sample | Easy to collect Close to researchers location |
| Stratified sample | Subgroups (2 of them) Same characteristics Draw same amt of sample from each Consistent |
| Cluster sample | Divide into groups Select only some groups Choose all elements from selected group Faster and less expensive |
| Multistage sample | Combination of methods Select sample in each stage Each stage different method Natural clusters |
| Reason for Frequency Tables | 1)summarize large data 2)analyze nature 3)basis for graphs |
| Relative Frequency | (Class frequency/sum of all frequency)x 100% |
| Unusual Center | Mean-2s or mean+2s |
| Coefficient of variation | (s/x)*100% |
| Bimodal | 2 modes |
| Multimodal | 2+ modes |
| Midrange | (max # - min#)/2 |
| Percentile | L(position)= k(percent)/100 *n |
| Interquartile | Q3-Q1 |
| 5 Number Summary(mon,q1,med,q3,max) | 1-Vars Stats |
| Odds against | P(not A)/P(A)-> A:B |
| Payoff odds | Net profit: amount of bet |
| Addition Rule of Probability | P(A or B)= P(A) + P(B) /total outcomes |
| Complements | P(none)= 1 - P(at least one) P(at least one) = P(only A or only B or both) = P(A only) + P(B only) - P(both) |
| Multiplication Rule (Independent) | P(A and B) = P(A) * P(B) |
| Multiplication Rule (Dependent) | P(A and B) = P(A) * P(B/A) after event A has occurred |
| Conditional Probability (Independent) | P(B/A) = P(A and B) / P(A) |
| Bayes' Theorem | P(A)*P(B/A) / [P(A)*P(B/A)]+[P(no A)*P(B/no A)] |
| Fundamental Counting Rule | m*n ways P(A) = 1/m*n |
| Permutation(different) | nPr n = # of items r = amt selected |
| Permutation(identical) | nPr = n!/ n1!n2!nk! |
| Combination Rule | nCr no repeats no order |
| Requirements for Probability Distribution | 1)Sum of P(x) = 1 2)0 < P(x) < 1 for every x |
| Probability mean | Sum of x * P(x) |
| Probability standard deviation | Square root of Sum of [(x^2 * P(x0]- mean^2 |
| Unusual Probability | P(x or more) < 0.05 P(x or fewer)< 0.05 |
| Binomial Distribution Requirements | 1)fixed # of trials 2)independent 3)2 categories 4)P(success)same in all success |
| Binomial Probability | binompdf(n,p(success),x success) |
| Binomial Mean | n*p(success) |
| Binomial Standard Deviation | sq. root of n*P(success)*P(failure) |
| Unusual values for Binomial | mean - 2stan. dev mean + 2stan. dev |
| Poisson Distribution Requirements | 1)x = event of interval 2)random 3)independent 4)uniformly distributed |
| Poisson Standard Deviaton | sq. root of mean |
| Using Poisson as Binomial Distribution Requirements: | 1)n > 100 2) np < 100 |
| Poisson Probability | poissonpdf(mean,x selected) |
| Normal Distribution Characteristics | 1)bell-shape 2)mean = 0 3) s = 1 |
| Uniform Distribution Characteristics | 1)area = 1 2) correspondence between area and prob |
| Normal Distribution (Area under graph) | normalcdf(left z,right z) |
| Z-score(normal distribution) | invNorm(area left of z-score) |
| Finding P(individual value) w/ Norm Distr | z = x - mean/ stan. dev |
| Finding P(sample) w/ Norm Distr | z = x - mean/ (stan dev./sq. root of n) |
| mean & x to z-score | normalcdf(left, right, mean, s)= P(x) invNorm(P(x))= z-score |
| Find x value of nonstandard norm distr | invNorm(area to left, mean, s) |
| Sample Variance | Sum(x - mean)^2 / n -1 mean = sum of x/n |
| Normal Distr As Binomial Approximate Requirements | 1)independent simple random sample 2)np> 5 and nq>5 |
| Continuity Correction | x - 0.5 to x + 0.5 |
| P(Area to left) | normalcdf(-99999,z-score) |
| Normal Distribution on Graph | 1)straight line 2)no systematic pattern |
| Find Critical Value(z-score) | 1-(confidence interval/2)-->invNorm(1-alpha) |
| Margin of Error (z-score) | z(alpha/2) * sq. root(p(success)*q(failure)/n) or upper CI - lower CI/ 2 |
| Confidence Interval(z- score) | Stat--> 1-PropZInt |
| P(Success) | upper CI + lower CI/ 2 |
| Sample Size(independent) | n = (z(alpha/2)^2 *p*q)/E^2 or n = (z(alpha/2)^2 *p*q*.25)/E^2 |
| Margin of Error(stan. dev known) | ZInterval Set mean = 0 |
| Sample Size(stan dev known) | n= [z(alpha/2)*stan.dev/E]^2 |
| t statistic | invT(1-alpha,df=n-1) |
| Confidence interval(t-score) | TInterval |
| T-Score Properties | 1)norm distr 2)different t for different n 3) mean = 0 4)stan. dev. > 1 5)n increase, t --> norm distr |
| Chi-Square Distribution Properties | 1)not symmetric 2)positive values 3)different for each df |
| Finding Chi-Square | 1)calculate alpha and df 2)What kind of test? 3)Look at Tables given |
| Confidence interval(chi-square) | sq.root[(n-1)s^2/chi right] < stan. dev < sq. root[(n-1)s^2/chi left] |
| Reject null (p-value) | p-value < alpha |
| Find p-value | normalcdf(left, right) |
| Reject null (test statistics) | test statistic falls in critical region bounded by critical value |
| Reject null(confidence interval) | Confidence interval does not contain claimed value |
| Type 1 Error | null true --> reject (alpha) |
| Type 2 Error | null false --> fail to reject (beta) |
| Two Tail Test | null = alternate not = |
| Right Tail Test | null = alternate > |
| Left Tail Test | null = alternate < |
| Testing Claim of Proportion | 1-PropZTest |
| Test Claim on Mean (stan. dev known) | Z-Test |
| Test Claim on Mean (stan dev Unknown) | T-Test |
| Test on 2 Proportions | 2-PropZTest |
| Confidence Interval(2 Proportions) | 2- PropZInt |
| Test on 2 Means (stan. dev. unknown/ independent) | 2-SampTTest 2-SampTInt |
| Test on 2 Means(Stan dev known) | 2-SampZTest 2-SampZInt |
| Claim on Mean (Dependent/differences) | 1) L1 - L2 2)TTest 3)TInt |
| Compare Variation of 2 Samples | 2-SampFTest |
| Correlation | 1)Straight-line 2) r = LinRegTTest 3) r > critical value of alpha 4) reject null |
| Regression | LinRegTTest |
| marginal change | slope of regression line |
| Residual | observed y - predicted y y from table - y from regression line |
| Coefficient of determination | r^2 |
Created by:
mnguye2
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