MA116 Midterm 1 | Questions And Answers | 100% Correct Answers Rated A+

Skewed right- 1. Long ____ tail 2. Mean and median relationship 3. Box and whiskers plot - where is the median? - ANS1. Right 2. Mean>Median 3. Toward right of box Skewed left- 1. Long ____ tail 2. Mean and median relationship 3. Box and whiskers plot - where is the median? - ANS1. Left 2. Mean<Median 3. Toward left of box Independence rules (3) - ANS1. P(A∩B) = P(A) * P(B) 2. P (A∩B/B) = P(A) 3. P (A∩B/A) = P(B) True or false- Disjoint events are independent - ANSFALSE- not always independent Permutations rule- does order matter? replacement? - ANSYes. Yes. Permutations and combinations rule: - N= - n= - ANS-N= Total elements -n= # in group Permutations formula - ANS(N!) / (N-n)! Combinations rule- does order matter? replacement? - ANSNo. No Combinations formula - ANS(N!) / n! (N-n)! Random variables (Mean, Standard Deviation) - ANS(sample mean, σ/√n) PDF- total area under curve= - ANS1 What is the probability that a continuous random variable is equal to any single point? - ANS0 General normal v. standard normal distributions- relationship between mean, median, and mode - ANSGeneral normal: mean=median=mode Standard normal: mean=median=mode=0 Qualities of a binomial distribution (4) - ANS-N IDENTICAL trials -2 possible mutually exclusive outcomes -P(success) remains the same form trial to trial -Independent trials Binomial distribution - ANSX~Bin (n,p) Bernoulli distrbution - ANSBin(1,p) = Ber(p) Binomial distribution- mean - ANSnp Binomial distribution- standard deviation - ANS√npq Binomial distribution- shape - ANS- p<.5= right skewed -p=.5= symmetric -p>.5= left skewed Normal distribution- if z-score is greater or less than +- 3.49 - ANSP= 0 or 1 depending on problem Percentiles: formula - ANSP(Z≤zp)=p p= - ANSPercentile (ex. 80th percentile) How to get zp - ANSPlug .8 inside Z-table. Get Z-score. Then transform. Normal approximation to the binomial- what must you check? - ANSnpq>10 Normal approximation to the binomial- What is very important to remember? - ANSThe ±.5 issue Normal approximation to the binomial- What letter do we use? - ANSY Normal approximation to the binomial- P(X=A) - ANSP(A-.5<Y<A+.5) Normal approximation to the binomial- P(X≤A) - ANSP(Y<A+.5) Normal approximation to the binomial- P(X<A) - ANSP(Y<A-.5) Normal approximation to the binomial- P(X≥A) - ANSP(Y>A-.5) Normal approximation to the binomial- P(X>A) - ANSP(Y>A+.5) Normal approximation to the binomial- P(A≤X≤B) - ANSP(A-.5<X<B+.5) Normal approximation to the binomial- P(A<X<B) - ANSP(A+.5<X<B-.5) Normal approximation to the binomial- What is unusual? - ANS<.05 Chi squared properties (2) - ANS-Skewed right -Depends on degrees of freedom Chi squared distribution- relationship between degrees of freedom and symmtery - ANS↑ DF, ↑ symmetry T-distribution properties (3) - ANS-Symmetric, but fatter -Depends on degrees of freedom -Similar to Z when N>30 Z-transform for sampling mean (point estimation) - ANS(x-µ) / (σ/√n) Sampling distribution for mean - ANSX~N (µ,σ) Conditions for point estimation for proportion - ANS-SRS -NPQ>10 -Independence= n<N.05 Point estimation for proportion- test statistics - ANS(Phat - Po) / √PoQo/n Confidence interval in English - ANS-We are ___% confident that the true unknown value of (µ, p, etc) is between (___,___). -If we construct 100 intervals, 95 percent of them will contain (µ, p, etc). Confidence interval- variance/sd-- Relationship between N and CI - ANS↑N, ↓Width of CI Type 1 error - ANSHo is rejected when it is true Type 2 error - ANSHo is NOT rejected when it is false