• Shuffle
Toggle On
Toggle Off
• Alphabetize
Toggle On
Toggle Off
• Front First
Toggle On
Toggle Off
• Both Sides
Toggle On
Toggle Off
Toggle On
Toggle Off
Front

Right/Left arrow keys: Navigate between flashcards.right arrow keyleft arrow key

Up/Down arrow keys: Flip the card between the front and back.down keyup key

H key: Show hint (3rd side).h key

A key: Read text to speech.a key

Play button

Play button

Progress

1/232

Click to flip

232 Cards in this Set

• Front
• Back
 What does RV stand for? random variable What are RV? they are numerical variables What are (2) types of RVs? (1)discrete (2)continous NAME this includes two types: discrete and continous RVs T or F RVs can be categorical false Can RVs be catergoical? no What are discrete numbers? are countable values only NAME these are countable variables only discrete varaible What are continous variables? are uncountable values such as fractions and decimals NAME these are uncountable values such as fractions and decimals continous variables How do u find the mean of RV? u=E(x)=∑x*P(x) How do u find the mean of RV? u=E(x)=∑x*P(x) How do u find the mean of RV? u=E(x)=∑*P(x) What does E(x) stand for? expected value of x What does E(x) stand for? expected value of x How do you find the variance of a discrete RV? (2) σ^2=E(x-u)^2= x^2*P(x)-u^2 (2) σ=√x^2*P(x)-u^2 How do you find the variance of a discrete RV? (2) (1)σ^2=E(x-u)^2= x^2*P(x)-u^2 (2)σ=√x^2*P(x)-u^2 What does σ stand for? variance Let x equal the number of cars owned by a family in Gainsville Using graph 1, (1)find the u of the r*vx (2)find the σ and σ^2 for rvx (3)Find P[u -2σu+2σ] (4)How many / what percentage of points can be found in the above range? (1)u=1.95 0.1(0)+.2(1)+.3(4)+.3(9)+.05(6)+.05(16)+.05(25) u=2.15 (2) σ^2= ∑x^2P(x) 0^2(.1)+1^2(.2)+(2)^2(.3)+3^2(10.3)+4^2(.08)+5^2(.05)- (2.15)^2 σ^2=1.53 and σ= 1.23 (3) P[2-22+2] P[04] (4).1+.2+.3+.3+.05= .95 Therefore, 95% of the population has one to 4 cars The bionomial distrubtubtion is (1) discrete RV The (1)ditrubtion is a discrete RV bionomial How many outcomes does a bionomial experiment have? 2 What are the outcomes of a binomial experiment? (2) (1) success (2)failure NAME this has two outcomes success and failure bionomial In a bionomial experiment there are (1)trials n independent The bionomial experiment can also be called (1) bernollie trails The (1)can also be called the bernollie trails binomial experiment The P(sucess) is (1) p The P of(1)is p sucess What is the P of sucess? p What is the P of failure? q P(failure) is (1) q What does q represent? the P of failure What does p represent? the P of sucess What is the sum of p and q? 1 The (1) of p and q is 1 sum p + q = (1) 1 The bionomial experiment can also be called (1) the Bernollie trails The (1)can also be called the Bernollie trails binomial experiment What is the rv x represent? the number of sucesses NAME this represetns the number of sucesses rv x T or F the P of sucess remains constant throughout the experiment true Does the P of sucess remain constant throughout the experiment? yes You have a jar of full of marbles. Each time you pick out a marble you do not put it back into the jar. Use graph 2, Suspose the x you want to find the # of not green marbles (1)what is the experiment? (2)is this a binomial experiment? (1)experiment= not green (2)P(G)=6/19=32% P(Y)=10/19=53% P(R)=3/19=16% P(NOT green)= 69% 2nd time= P(G)=6/18 P(NOT green)=1-(6/8)=66% No it is not a binomial bc p is not constant What are the (4) properties of binomail trails? (1)the binomial RV is a discrete (2)The binomail RV has 2 outcomes: sucess and failure (3)The rv variable x represents the number of sucesses (4)The P of sucess remains constant throughout the experiment NAME this has 4 main properties: (1)the binomial RV is a discrete (2)The binomail RV has 2 outcomes: sucess and failure (3)The rv variable x represents the number of sucesses (4)The P of sucess remains constant throughout the experiment bionomail traisl How do you find the binomail P by hand? P(x)=n(xP^x(1-P)^n-x x=0,1,2,..n How do you find the binomail P by hand? P(x)=n(xP^x(1-P)^n-x x=0,1,2,..n How would you solve for 3!? 3*2*1=6 How would you solve for 5!? 5*4*3*2*1=120 How would you solve for 6!? 6*5*4*3*2*1=720 What does 1! ? 0 What does 0!? 0 In you calculator, how do u find symbol ! ? (3) Go to math (2)PRB (3)Select 4 What does nCx stand for? combination What does combination? means the arrangement of n objects taking x of them at a time disregarding order the following terms, difference and not equal to can indicate (1)type of hypothesis testing both sided testing What is the symbol for combination? nCx Given (a,b,c) arrange them in combinations of 2 (ab, ac, bc) What is the formula for nCx ? nCx= (n!)/[x!(n-x)!] What is the formula for nCx? nCx=(n!)/[x!(n-x)!] Given (a,b,c) (1)arrange them in combination of 2 (2)Find how many combinations (1)(ab,ac,bc) (2)3!/2!(3-2)!= 3!/2!=3 T or F for permetation order is not important false For permetation, is order important? yes For combination order is important? no T or F for combination order is important true How do you tell the differ btwn combination and permetation? (1)combination= order is not important (2)permetation=order is important What is Permetation? is the arrangement of n objects taking x of them at a time in a distinct order NAME is the arrangement of n objects taking x of them at a time in a distinct order permetation Permete 3 groups of (a,b,c)in groups of 2 answer= (ab,ba) ca,ac,bc,cb How do u find a binomial distrubution? (3) (1)P(x)=nCxP^xq^n-x (2)q=1-P (3)x=0,1,2,..n (4)n=# of people etc How do you find a binomial distrubtion? (3) (1)P(x)=nCxP^xq^n-x (2)q=1-P (3)x=0,1,2,..n There is a revolutionary technique of heart surgery at Shands hospital. The rate of success of this technique is 80%. If five people undergo this surgery, what is the P that (1)none of them will survive n=5 x=# of surviors P=.8 q=.2 x=0,1,2,3,4, and 5 (1)P(x)= nCxP6xq^n-x q=1-P P(0)=5C0(.8)^0(.2)^5-0 P(0)=(1)(1)(3.2*10^-4) P(0)=3.2*10^-4 There is a revolutionary technique of heart surgery at Shands hospital. The rate of success of this technique is 80%. If five people undergo this surgery, what is the P that (1)that all of them will survive P(x)=nCxP^xq^n-x n=5 x=# of surviors= 0,1,2,3,4 and 5 p=.8 q=1-.8=.2 (1)P(5)=5C5(.8)^5(.2)^(5-5) P(5)=(1)(.32)(1) P(5)=.32 There is a revolutionary technique of heart surgery at Shands hospital. The rate of success of this technique is 80%. If five people undergo this surgery, what is the P that (1)at least one of them will survive P(x)=nCxP^xq^n-x n=5 x=# of surviors= 0,1,2,3,4 and 5 p=.8 q=1-.8=.2 (1) P(1,2,3,4,5)=1-P(0) P(0)=5Co(.8)^0(.2)^5-0 P(0)=(1)(1)(3.2*10^-4) P(0)=3.2*10^-4 P(1,2,3,4,5)= 1-3.2*10^.4 P(1,2,3,4,5)=.9997 There is a revolutionary technique of heart surgery at Shands hospital. The rate of success of this technique is 80%. If five people undergo this surgery, what is the P that (1)At most 3 of them will survive P(x)=nCxP^xq^n-x n=5 x=# of surviors= 0,1,2,3,4 and 5 p=.8 q=1-.8=.2 (1)P(1,2,3)=1-P(4 and 5) P(4)=5C4(.8)^4(.2)^5-4 P(4)=(5)(.410)(.2)= p(4)=.41 P(5)=5C5(.8)^5(.2)^(5-5) P(5)=(1)(.32)(1) P(5)=.32 SOLUTION: P(1,2,3)=1-(.41+.32)=.27 P(1,2,3)=.27 There is a revolutionary technique of heart surgery at Shands hospital. The rate of success of this technique is 80%. If five people undergo this surgery, what is the P that (1)Exactly 2 of them will survive P(x)=nCxP^xq^n-x n=5 x=# of surviors= 0,1,2,3,4 and 5 p=.8 q=1-.8=.2 (1) P(1,2)= P(2)=5C2(.8)^2(.2)^5-2 P(2)=(10)(.64)(.008) p(2)=.0512 There is a revolutionary technique of heart surgery at Shands hospital. The rate of success of this technique is 80%. If five people undergo this surgery, what is the P that (6)Find the mean and standard deviation of the number of people who survived language between *be careful*between (1)3-5=4 (2)2-5=3,4 (3)1-5=2,3,4 The mean of a binomail rv is given by (1) u=NP The varaince of a binomial is given by (1) σ^2=npq How do you use your Calculator to find the binomial distrubtion? (1) 2nd distrubtion binompdf(n,p,{x} (2)FOR MULTIPLE VALUE 2nd distrubtion A>binomacdf(n,p{x}) There is a revolutionary technique of heart surgery at Shands hospital. The rate of success of this technique is 80%. If five people undergo this surgery, what is the P that Using you Calculator- (1)none of them will survive (1)binocmcdf(5,.8{0})=.32 There is a revolutionary technique of heart surgery at Shands hospital. The rate of success of this technique is 80%. If five people undergo this surgery, what is the P that Using your calculator (1At most 3 of them will surive (1) P(x≥2)=P(3,4,5)=1-P(x≤2) 1-binocmcdf(5,.8{2})=.94208 There is a revolutionary technique of heart surgery at Shands hospital. The rate of success of this technique is 80%. If five people undergo this surgery, what is the P that (1)find the mean of the binomial rv (2)Find the variance of the binmomial rv (1) u=np u5*.8=4 (2)σ^2=npq σ^2=(5)(.8)(.2)=.8944 What is statistic? is a descriptive measure obtained from the sample NAME this is a descriptive measure obtained from the sample statistic What is a parameter? is a descriptive measure obtained from the pop NAME this is a descriptive measure obtained from the pop parameter What is the differ btwn the statistic and parameter? (1)statistic=a descriptive measure obtained from the sample (2)parameter=a descriptive measure obtained from the population What are (2)types of statics? (1)descriptive Stats (2)inferential Stats NAME there are 2 types:descriptive Stats and inferential stats stastics What are descriptive stastics? they use graphs affected by personal opinons NAME this uses graphs affected by personal opinions descriptive stastics What is inferential stastics? use mathmatical formulas not as influenced by opinion NAME they use mathmatical formulas not as influenced by opinion inferential stastics What is the differ btwn descriptive stastics and infeerential stastics? (1)inferentials stastics=use mathmatical formulas not as influenced by opinion (2)descriptive stastics=they use graphs affected by personal opinons - In Stastics, x is the mean. However, in the population parameter, (1) is the mean u In Stastics, (1)is the mean. However in the population parameter, the u is the mean - x In stastics, s^2 represents the sample variance. However for population parameter, (1)represents the sample variance σ^2 In stastics, (1)represents the sample varaince However for population parameter, the σ^2 represents the sample variance s^2 What does σ represent? the pop variance In stastics, s represents the standard deviation. However, for pop parameter (1)represents the standard deviation σ In stastics, the (1)represents the standard deviation. However, for the pop parameter, σ represents the standard deviation s if x is disturbed normally then (1) the mean is distrubed normally w σ/√n If x is distrubed (1)then the mean is distrubed normally w σ/√n normally What does the symbol ~ represent? distrubtion What does the symbol N represent? normal (Use symbols) If x is distrubed normally then (1) mean~N(u.σ/√n) even if x is disturbed noramlly, the histogram of the mean will be (1) symmetric or normal What is the central limit theorem? if RV x is not distrubed normal the distruption of the mean is normal (2)for n >30, as n increases the graph gets more normal NAME if RV x is not distrubed normal the distruption of the mean is (1) normal SUpose you sample from a non-normal distrubtion of a RV x w mean (u) in standard devieation then for large N, the mean is (1) distrubed normal and the standard deviation is σ/√n for n>30, as n increases the graph gets (1) more normal - x~?(u,σ) then (1) - x~N(u,σ/√n_ - (1)then x~N(u,σ/√n_ - x~?(u,σ) Find P(600800) when u= 550 and σ =100 normalcdf lower=600 upper=800 mean=500 σ =σ /√n ^ What is the mean of p ? P ^ What is the mean of p ? p The average students in a stat class for 10 years is 82 students and the σ =5. The current class has 37 students. What is the P (7487) normalcdf lower=74 upper=87 mean=82 σ =σ /√n when n= 37 The average students in a stat class for 10 years is 82 students and the σ =5. The current class has 37 students. What is the P(mean>92) lower=92 upper=200 mean=82 σ =σ /√n when n= 37 The average students in a stat class for 10 years is 82 students and the σ =5. The current class has 37 students. What is the P (mean<72). 0 What is the mean of z=0? 0 What is standard deivation the of the z score? 1 What is the mean of z? 0 What is the standard deviation of z? 1 The average students in a stat class for 10 years is 82 students and the σ =5. The current class has 37 students. What is the P(-9.756.08) normalcdf lower=-9.75 Upper=6.08 Mean=0 σ =1 Convert the following P score into a z score. P(7487) 74-82/ (5/√37)= 87-82/ (5/√37) solution= -9.75 and 6.08 Mr tec knows that of all of the students who take STA 2023 4% fail the class. This year he had a class of 37 students. (1)find P(.003

.005) normal cdf lower=.03 upper=.005 mean=.04 σ =√pq/n=.001 Mr tec knows that of all of the students who take STA 2023 4% fail the class. This year he had a class of 37 students. Find P(p hat>0.06) normal cdf lower=.06 upper=1 mean=.04 σ =√pq/n=.032 Solution Mr tec knows that of all of the students who take STA 2023 4% fail the class. This year he had a class of 37 students. Find P hat <.03) normal cdf lower=0 upper=.03 mean=.04 σ =√pq/n=.001 if ux=10 and Uy=20. What is E(x+y) E(10+20)=30 if uy=80. What is E(x+10)? 90 Var x= 10 Var y=20 What is var(x+y)? 22 If ux=80 what is Var(10x)? 800 find Var(10x)2hen x=100? 10^2var100=1000 Find σx for var(10x)? a√varx=10√10 How do you tell if u use a small sample size? if n or both n's are smaller than 30 How do you tell if you use a big sample size? if n or both n's are bigger than 30 How do u know when to use t distrubtion? is you have a small reference frame and (2)pop variance is uknown Draw a graph explaining what alpa is? see graph 1 if the area you are looking for is .95? what is aplha? 1-.95=.05 How do you find z*? Invnorm(area,0,1) If p and q are not given, what are u to assume there value is? both are .5 If p and q are not given, what are u to assume there value is? both are .5 if you increase the pop variance, then the ME (1) increases ME stands for (1) margion of error What does E stand for? random variable If you increase n then the ME (1) decreases If you increase z* then the ME (1) increases When do you use the T-interval test? (2) (1)if n or both n's are less than 30 (2)and the pop variance is unkown When do you pool data or not? if pop variance1^2=pop variacnce2^2 then you pool the data otherwise you dont How do you tell if u use a small sample size? if n or both n's are smaller than 30 How do you tell if you use a big sample size? if n or both n's are bigger than 30 How do u know when to use t distrubtion? is you have a small reference frame and (2)pop variance is uknown Draw a graph explaining what alpa is? see graph 1 if the area you are looking for is .95? what is aplha? 1-.95=.05 How do you find z*? Invnorm(area,0,1) How do you tell if u use a small sample size? if n or both n's are smaller than 30 If p and q are not given, what are u to assume there value is? both are .5 How do you tell if you use a big sample size? if n or both n's are bigger than 30 If p and q are not given, what are u to assume there value is? both are .5 How do u know when to use t distrubtion? is you have a small reference frame and (2)pop variance is uknown if you increase the pop variance, then the ME (1) increases Draw a graph explaining what alpa is? see graph 1 if the area you are looking for is .95? what is aplha? 1-.95=.05 How do you find z*? Invnorm(area,0,1) If p and q are not given, what are u to assume there value is? both are .5 If p and q are not given, what are u to assume there value is? both are .5 if you increase the pop variance, then the ME (1) increases ME stands for (1) margion of error What does E stand for? random variable If you increase n then the ME (1) decreases If you increase z* then the ME (1) increases When do you use the T-interval test? (2) (1)if n or both n's are less than 30 (2)and the pop variance is unkown When do you pool data or not? if pop variance1^2=pop variacnce2^2 then you pool the data otherwise you dont ME stands for (1) margion of error What does E stand for? random variable If you increase n then the ME (1) decreases If you increase z* then the ME (1) increases When do you use the T-interval test? (2) (1)if n or both n's are less than 30 (2)and the pop variance is unkown When do you pool data or not? if pop variance1^2=pop variacnce2^2 then you pool the data otherwise you dont What is a hyptothesis? is a educated guess NAME this is a educated guess hypothesis What is the symbol for the hypothesis? ho What is hypothesis testing? is a claim or statement about the distrubtion of a certain population using respective parameteres NAME this is a claim or statement about the distrubtion of a certain population using respective parameters hypothesis testing If you make a claim that the class average will be 85 what are the (3)altervative hypothesises? What test would u use to find the answer? (1)u is > 80 (2) u is ≠ 80 (3)u<80 (4)z test what is a null hypothesis? is the hypothesis that the researcher hopes to disprove NAME this is the hypothesis that the reseracher hope to disprove null hypthesis What is symbol for the null hypothesis? Ho What does Ho represent? the null hypothesis If you make a claim that the class average will be 85. what is the Ho and Ha? (2) (1)Ho=u=85 (2)Ha= u ≠ 85 u > 85 u < 85 What is the alternative hypothesis? is the hypothesis that the researcher hopes to proove NAME this is the hypothesis that the researcher hopes to prove alternative hypothesis What is the symbol for the alternative hypothesis? Ha What does the symbol Ha represent? the alternative hypothesis What are the main elements of hyothesis testing? (4) (1)state Ho (2)state Ha (3)Test stastics (either z or t test) (4)make descicion (reject or accpet Ho) Draw a pic of how to tell what the rejection region is for right sided hypothesis testing? see graph 2 Draw a pic of how to tell what the rejection region is for left sided hypothesis testing? See graph 3 if u are using right sided hypothesis testing then ha is (1) u > uo If you are using left sided hypothesis testing then Ha is (1) u < uo If you are using not sure if the testing should be left or right sided testing then Ha is (1) u>uo and (2)u alpha then you accept Ho (3)also if p is a very very small number you can conclude that Ho would be rejected if p ≤ aplha then you (1) Ho reject If p > alpha then you (1)Ho accpet If p is a very small number then you (1)Ho reject How do you find p by hand? Find the P(z>zdata) then us normal cdf lower=z data upper=a big number greater than z data mean=0 varaince=1 What is the z way? Find z* and compare it to z data result depends on type of testing whether-right or left sided What are (2)types of errors/ (1)type I (2)type II What is type I error? when you reject Ho when the null is actually true NAME this is when you reject Ho when the null is actually true type I error What is type II error? this is when you accept a false Ho NAME this refers to when you accept a false Ho type II error What is the def of alpha in context of hypothesis testing? is the P of rejecting Ho when it is true NAME this is the P of rejecting Ho when it is true aplpha in context of hypothesis testing What is beta? isthe P of accepting a false Ho NAME this is the P of accepting a false Ho beta Supose Ho=the person is innocent Ha=the person is guilty the guilty person is exucated Which type of error is worse? type I Supose Ho:the market goes up Ha:the market goes down and you are going to invest in the market based on the results of the test (1)What does each error say (2)which errors is worse? (1)dont lose money (2)type II-lose money (2)type II bc u lose your money the null hypothesis can also be called the (1) the hypothesis of no affect or difference The (1)hypothesis can also be called the the hypothesis of no affect or difference null The alternative hypothesis can also be called the (1) researcher hypothesis The (1)hypothesis can also be called the researcher hypothesis alternative How do u find z*? (2) (1)InvNorm (1-alpha/2, 0,1) or (2)InvNorm (alpha/2,0,1)= but will be a negative number