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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(xu)^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(xu)^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 2σ<x>u+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[22<x>2+2] P[0<X>4] (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(1P)^nx
x=0,1,2,..n 

How do you find the binomail P by hand?

P(x)=n(xP^x(1P)^nx
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!(nx)!]


What is the formula for nCx?

nCx=(n!)/[x!(nx)!]


Given (a,b,c)
(1)arrange them in combination of 2 (2)Find how many combinations 
(1)(ab,ac,bc)
(2)3!/2!(32)!= 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^nx
(2)q=1P (3)x=0,1,2,..n (4)n=# of people etc 

How do you find a binomial distrubtion? (3)

(1)P(x)=nCxP^xq^nx
(2)q=1P (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^nx q=1P P(0)=5C0(.8)^0(.2)^50 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^nx
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)^(55) 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^nx
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)=1P(0) P(0)=5Co(.8)^0(.2)^50 P(0)=(1)(1)(3.2*10^4) P(0)=3.2*10^4 P(1,2,3,4,5)= 13.2*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^nx
n=5 x=# of surviors= 0,1,2,3,4 and 5 p=.8 q=1.8=.2 (1)P(1,2,3)=1P(4 and 5) P(4)=5C4(.8)^4(.2)^54 P(4)=(5)(.410)(.2)= p(4)=.41 P(5)=5C5(.8)^5(.2)^(55) 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^nx
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)^52 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)35=4 (2)25=3,4 (3)15=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)=1P(x≤2) 1binocmcdf(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 nonnormal 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(600<mean>800)
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 (74<mean>87)

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(9.75<z>6.08)

normalcdf
lower=9.75 Upper=6.08 Mean=0 σ =1 

Convert the following P score into a z score.
P(74<mean>87) 
7482/ (5/√37)=
8782/ (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<P hat>.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 Tinterval 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 Tinterval 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 Tinterval 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<uo


the following terms,
more than, better than, and greater than can indicate (1)hypothesis testing 
right sided


The terms
(1),(2), and (3), can indicate right sided hypothesis testing 
right sided


What are (2)ways to tell if you reject or accept Ho?

(1)the z way (2)the p way


The terms,
less than, not equal to, the difference can indicate (1)hypothesis testing 
left sided


The terms,
(1), (2), and (3) can indicate left sided hypothesis testing 
(1)not equal (2)difference (3)less than


What are (2)ways that you tell to reject or accept the Ho?

(1)the Z way (2)P way


Z* can also be called (1)

z critical


(1) can also be called z critical

z*


What is the P way?

(1)if p ≤ aplha then you reject Ho
(2)if p > 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 whetherright 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 IIlose 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 (1alpha/2, 0,1)
or (2)InvNorm (alpha/2,0,1)= but will be a negative number 