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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