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by: Aishwarya Juttu

StatsforScience_FinalStudyGuide Math 3339

Marketplace > University of Houston > Mathematics (M) > Math 3339 > StatsforScience_FinalStudyGuide
Aishwarya Juttu

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About this Document

This study guide contains a summary of the final review, r-codes & formulas
Statistics for the Sciences
Prof. C Poliak
Study Guide
UH, Stats, Math, final study guide
50 ?




Popular in Statistics for the Sciences

Popular in Mathematics (M)

This 4 page Study Guide was uploaded by Aishwarya Juttu on Tuesday July 19, 2016. The Study Guide belongs to Math 3339 at University of Houston taught by Prof. C Poliak in Summer 2016. Since its upload, it has received 21 views. For similar materials see Statistics for the Sciences in Mathematics (M) at University of Houston.


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Date Created: 07/19/16
Important concepts to know: R studio for binomial • P(X=k) use dbinom(k,n,p) • P(X ≤ k) use pbinom(k,n,p) • P(X >k) use 1-pbinom(k,n,p) R studio for z-scores • P(Z ≤ x) use pnorm(x) • P(Z ≥x) use 1-pnorm(x) • P(x<Z<y) use pnorm(y)-pnorm(x) • If mean and sd are given then use pnorm(x,μ,σ) or pnorm(x,μ,σ,prob/sqrt(n)) Critical value • To find z-score use z-table or qnorm((1 + c)/2) • To find t-score use t-table or qt((1+c)/2,df) Rejection region • Using z-score: qnorm(α) • Using t-score: qt(α,df) Chi squared confidence interval lcl=n-1*var/qchisq((1+c)/2,(n-1)) if sd is given, square it because sd^2=var • • ucl=n-1*var/qchisq((1-c)/2,(n-1)) • Var: c(lul,ucl) • SD: sqrt(c(lul,ucl)) To interpret confidence interval:
 • Write down all given values (average, sample size, margin of error)
 • +&- the margin of error from the average, it will give you the interval with an upper value and a lower value
 • Write the interpretation: We are % confident that the question is between lower value and upper value • R code for Proportions Confidence Interval: pˆ+c(-1,1)*qnorm(1+c/2)*sqrt(pˆ*(1-pˆ)/100) • R code for Mean Confidence Interval when population sd is unknown: µ+c(-1+1)*qt((1+c)/2, (n-1))*s/sqrt(n)  Probability Rules 1. P(E) has to be between 0 and 1 2. P(Ω)= 1 3. There are no elements inA&B= pairwise disjoint 4. Complement Rule- P(~A)= 1-P(A) 5. P(Ø)= O no elements 6. Addition Rule- P(AuB)= P(A)+P(B)-P(AnB) when finding the chance of eventsAor B 
 happening 7. Multiplication- P(AnB)= P(A) x P(B, givenA) OR P(AnB)= P(B) x P(A, given B) when 
 finding the chance of events ofAand B happening 8. Conditional probability- P(A,given B)=(P(AnB))/(P(B)) 
 Permutations- computing number of outcomes where order does matter • nPr= (n!)/(n-r)!
 • P= (n!)/[(r!)(s!)(t!)] for repeating letters Circular•permutations- (n-1)! Combinations- counts number of outcomes where order doesn’t matter nCr=(n!)/(r!(n-r)!) •     • σ^2= var(X) • mean=E(X)=∑(X*P(X)) • var(X)=E(X^2) - [E(X)]^2 • E(X^2)= (X^2)*(P(X)) • Remember in probability distribution table, P(X)=1 
 Chi squared statistic test • First name<-matrix(c(x1,x2,x3,y1,y2,y3),nrow=#ofx,ncol=#ofy) • Second name • Third chisq.test(name) - Chi-square contribution- residuals(chisq.test(matrix,correction=FALSE))^2 Chi squared good-fitness test • chisq.test(c(list of observed values),p = c(list ofproportions)) • If list of proportions is not give, then chisq.test(c(list of observed values),p = c(list ofproportions)) Two sample t test • R code from t score to p value, two tailed: 2*pt(t,df) - Anova-Analysis of variance- determines whether there is more variance among the sample means than we would expect - Mean square for treatments- MSTr= SSTr/N-M - Mean square for error- MSE= SSE/M-1 - Test statistic- F= MSTr/MSE • p-value= 1-pf(f,M-1,N-M) - Two population problems- used to compare the responses in two groups, each group is a sample from a distinct population and the responses must be independent of those in the other group • Both samples must be independent SRS from the population of interest • Both sets must be from normally distributed populations - Two-sample t test- used if both population sd are unknown If p value is less than alpha, then reject Ho If p value is more than alpha, then fail to reject Ho


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