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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(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 -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[2-2<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(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(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)
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<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 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<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 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