### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# StatsforScience_FinalStudyGuide Math 3339

UH

### View Full Document

## About this Document

## 21

## 0

## 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.

## Popular in Mathematics (M)

## Reviews for StatsforScience_FinalStudyGuide

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

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

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "When you're taking detailed notes and trying to help everyone else out in the class, it really helps you learn and understand the material...plus I made $280 on my first study guide!"

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.