year 13 statistics & modelling workshop department of statistics house sales what proportion of...
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YEA
R 1
3 S
TA
TIS
TIC
S &
MO
DELL
ING
W
OR
KSH
OP
DEPARTMENT OF STATISTICS
House Sales
What proportion of the houses that sold for over $600,000 were on the market for less than 30 days?
Days on the market
Less than 30 days
30 - 90 days More than 90 days
Under $300,000 39 31 15 85
$300,000 - 600,000 35 45 4 84
Over $600,000 8 4 0 12
82 80 19 181
Selling price Total
Total
YEA
R 1
3 S
TA
TIS
TIC
S &
MO
DELL
ING
W
OR
KSH
OP
DEPARTMENT OF STATISTICS
Days on the market
Less than 30 days
30 - 90 days More than 90 days
Under $300,000 39 31 15 85
$300,000 - 600,000 35 45 4 84
Over $600,000 8 4 0 12
82 80 19 181
Selling price Total
Total
House Sales
What proportion of the houses that sold for over $600,000 were on the market for less than 30 days?
YEA
R 1
3 S
TA
TIS
TIC
S &
MO
DELL
ING
W
OR
KSH
OP
DEPARTMENT OF STATISTICS
Days on the market
Less than 30 days
30 - 90 days More than 90 days
Under $300,000 39 31 15 85
$300,000 - 600,000 35 45 4 84
Over $600,000 8 4 0 12
82 80 19 181
Selling price Total
Total
House Sales
What proportion of the houses that sold for over $600,000 were on the market for less than 30 days?
YEA
R 1
3 S
TA
TIS
TIC
S &
MO
DELL
ING
W
OR
KSH
OP
DEPARTMENT OF STATISTICS
House Sales
What is the probability a house sold for under $300,000 given that it sold in less than 30 days?
Days on the market
Less than 30 days
30 - 90 days More than 90 days
Under $300,000 39 31 15 85
$300,000 - 600,000 35 45 4 84
Over $600,000 8 4 0 12
82 80 19 181
Selling price Total
Total
YEA
R 1
3 S
TA
TIS
TIC
S &
MO
DELL
ING
W
OR
KSH
OP
DEPARTMENT OF STATISTICS
Days on the market
Less than 30 days
30 - 90 days More than 90 days
Under $300,000 39 31 15 85
$300,000 - 600,000 35 45 4 84
Over $600,000 8 4 0 12
82 80 19 181
Selling price Total
Total
House Sales
What is the probability a house sold for under $300,000 given that it sold in less than 30 days?
YEA
R 1
3 S
TA
TIS
TIC
S &
MO
DELL
ING
W
OR
KSH
OP
DEPARTMENT OF STATISTICS
House Sales
What is the probability a house sold for under $300,000 given that it sold in less than 30 days?
Days on the market
Less than 30 days
30 - 90 days More than 90 days
Under $300,000 39 31 15 85
$300,000 - 600,000 35 45 4 84
Over $600,000 8 4 0 12
82 80 19 181
Selling price Total
Total
YEA
R 1
3 S
TA
TIS
TIC
S &
MO
DELL
ING
W
OR
KSH
OP
DEPARTMENT OF STATISTICS
Blood Group Systems (Rh & K)
Rh system Kell system Outcome Probability
Rh+
Rh–
0.81
0.19
K+
K–
K+
K–
0.08
0.92
0.08
0.92
Rh+ K+
Rh+ K–
Rh– K+
Rh– K–
0.81 x 0.08
0.81 x 0.92
0.19 x 0.08
0.19 x 0.92
YEA
R 1
3 S
TA
TIS
TIC
S &
MO
DELL
ING
W
OR
KSH
OP
DEPARTMENT OF STATISTICS
Blood Group Systems (K & Rh)
Kell system Rh system Outcome Probability
K+
K–
0.08
0.92
Rh+
Rh–
Rh+
Rh–
0. 81
0.19
0.81
0.19
K+ Rh+
K+ Rh–
K– Rh+
K– Rh–
0.08 x 0.81
0.08 x 0.19
0.92 x 0.81
0.92 x 0.19
YEA
R 1
3 S
TA
TIS
TIC
S &
MO
DELL
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W
OR
KSH
OP
DEPARTMENT OF STATISTICS
ELISA: HIV Screening Test
98% true positive and 7% false positive
Suppose 1% of the population have HIV
Of those that test positive for HIV, what proportion have HIV?
1
0.99
0.01
Total
Not HIV
HIV
TotalNegativePositive
Test resultDisease
status
98% of 0.01
0.0098 0.0002
7% of 0.99
0.0693 0.9207
0.0791 0.9209
YEA
R 1
3 S
TA
TIS
TIC
S &
MO
DELL
ING
W
OR
KSH
OP
DEPARTMENT OF STATISTICS
ELISA: HIV Screening Test
98% true positive and 7% false positive
Suppose 1% of the population have HIV.
Of those that test positive for HIV, what proportion have HIV?
1
0.99
0.01
Total
Not HIV
HIV
TotalNegativePositive
Test resultDisease
status
0.0098 0.0002
0.0693 0.9207
0.0791 0.9209
YEA
R 1
3 S
TA
TIS
TIC
S &
MO
DELL
ING
W
OR
KSH
OP
DEPARTMENT OF STATISTICS
ELISA: HIV Screening Test
98% true positive and 7% false positive
Suppose 1% of the population have HIV.
Of those that test positive for HIV, what proportion have HIV?
1
0.99
0.01
Total
Not HIV
HIV
TotalNegativePositive
Test resultDisease
status
0.0098 0.0002
0.0693 0.9207
0.0791 0.9209
0.0098 / 0.0791 = 0.1239
YEA
R 1
3 S
TA
TIS
TIC
S &
MO
DELL
ING
W
OR
KSH
OP
DEPARTMENT OF STATISTICS
ELISA: HIV Screening Test
Why is the probability of having HIV given that the test is positive so low?
Proportion who don’t have HIV
(99%) Proportion who have HIV (1%)
YEA
R 1
3 S
TA
TIS
TIC
S &
MO
DELL
ING
W
OR
KSH
OP
DEPARTMENT OF STATISTICS
ELISA: HIV Screening Test
Why is the probability of having HIV given that the test is positive so low?
Proportion who have HIV (1%)
Positive testsProportion who don’t have HIV
(99%)
98% of 1%
YEA
R 1
3 S
TA
TIS
TIC
S &
MO
DELL
ING
W
OR
KSH
OP
DEPARTMENT OF STATISTICS
ELISA: HIV Screening Test
Why is the probability of having HIV given that the test is positive so low?
Proportion who have HIV (1%)
Proportion who don’t have HIV
(99%)
Positive tests
98% of 1%
7% of 99%
True
False
Many more false positives than true positives
YEA
R 1
3 S
TA
TIS
TIC
S &
MO
DELL
ING
W
OR
KSH
OP
DEPARTMENT OF STATISTICS
ELISA: HIV Screening Test
HIV
Not HIV
0.01
0.99
Disease status
Test result
0.98
0.02
0.07
0.93
Pos | HIV
Neg | HIV
Pos | Not HIV
Neg | Not HIV
HIV and Pos
HIV and NegNot HIV and Pos
Not HIV and Neg
Outcome Probability
0.98 x 0.01
0.02 x 0.010.07 x 0.99
0.93 x 0.99
Of those that test positive for HIV, what proportion have HIV?
P(HIV Pos) = P(Pos | HIV) x P(HIV)
YEA
R 1
3 S
TA
TIS
TIC
S &
MO
DELL
ING
W
OR
KSH
OP
DEPARTMENT OF STATISTICS
ELISA: HIV Screening Test
HIV
Not HIV
0.01
0.99
Disease status
Test result
0.98
0.02
0.07
0.93
Pos | HIV
Neg | HIV
Pos | Not HIV
Neg | Not HIV
HIV and Pos
HIV and NegNot HIV and Pos
Not HIV and Neg
Outcome Probability
0.98 x 0.01
0.02 x 0.010.07 x 0.99
0.93 x 0.99
Of those that test positive for HIV, what proportion have HIV?
YEA
R 1
3 S
TA
TIS
TIC
S &
MO
DELL
ING
W
OR
KSH
OP
DEPARTMENT OF STATISTICS
ELISA: HIV Screening Test
HIV
Not HIV
0.01
0.99
Disease status
Test result
0.98
0.02
0.07
0.93
Pos | HIV
Neg | HIV
Pos | Not HIV
Neg | Not HIV
HIV and Pos
HIV and NegNot HIV and Pos
Not HIV and Neg
Outcome Probability
0.98 x 0.01
0.02 x 0.010.07 x 0.99
0.93 x 0.99
Of those that test positive for HIV, what proportion have HIV?
99.007.001.098.0
01.098.0)Pos|HIV(P