MATHS IB Flashcards
GOF
Are the outcomes in proportion to expected or is there a bias
Example: flipping a coin (we would expect there to be 50 heads/50 tails)
If we flipped heads 80 times (did this come about by chance or is the coin biased)
Null: The coin is not biased (we should expect even outcomes)
Alternative: Observed data does not follow expected distribution
T test:
1 sample t-test:
Null hypothesis:mean of a single population is equal to a specified value
Alternative hypothesis: X1 > X2 OR X2 > X1
Two-sample t-test
Null hypothesis:
would be that the means of two populations are equal
Alternative hypothesis:
would suggest that the true means of the two populations are not equal.
How to find the expected value in a chi-squared test?
GDC –> MAT B –> ONLY AFTER DOING THE TEST
3sf
3sf
How to perform GOF
STAT –> LIST 1 (TYPE IN THE OBSERVED FREQUENCIES) –> LIST 2 (TYPE IN EXPECTED FREQUENCIES LIKELY TO HAVE BEEN CALCULATED)
TEST –> CHI –> GOF –> FIX DF –> EXECUTE
Scenario:
They have given a one tailed t-test.
Table:
Z N X Y
If they say that Y is supposedly bigger than X, what does th expression look like
Y > X
They can be switched around
Point slope form equation:
y-y1 = m(x-x1)
Point the line passes through (x,y)
What is the x intercept and y intercept
X intercept (where y = 0)
Y intercept (where X = 0)
Conditions for perpendicular bisector?
90’ right angle formed with the line it cuts through
Bisector –> it cuts halfway through
Discrete vs Continuos
Find the probability that at least one of the die rolls show white.
Do not forget to look at the first picks of White
Conditional Probability equation
P(A|B) = P(A and B) / P(B)
The probability of A given that the probability of B has already occured
Probability that Arsenal win the league given they beat city
Law of Total Probability
Pr(W)= Pr(R)⋅ Pr(W∣R)+ Pr(R’ )⋅ Pr(W∣R′ )
The probability of the complement of event A is calculated as:
P(A’) = 1 - P(A)
All set notation?
see
How to construct a probability distribution table?
see
How to convert percentage change into common ratio
% divided by 100 + 1
EG: 5.3/100 + 1
Is Normal Distribution continuos?
Continuos
Is Binomial Distribution discrete?
Discrete
P(x=20) =
(Normal Distribution)
0
You can not find the probability of one value in Normal Distribution
How to construct a bell curve
SEE
What is the Z score
Z = x - mean/SD
How many SD’s are you away from the mean
SD and data point relationship
2SD - 95%
1SD - 68%
3SD - 99.7%
How to find the sd on a calculator
see
How to find the range of a function
GDC –> THINK ABOUT INSIDE THE CURVE
IF THERE ARE TWO CURVES
THE ONE GOING UP (LOW–> HIGH)
THE ONE GOING DOWN LOW –> HIGH)
y = -3/2x + 24 to standard form step by step
To convert the equation y = -3/2x + 24 into standard form, follow these steps:
Move the x term to the left-hand side:
3/2x + y = 24
Multiply both sides of the equation by 2 to eliminate the fraction:
3x + 2y = 48
This is the equation in standard form, where A = 3, B = 2, and C = 48. Note that it’s common to write the equation in standard form with integer coefficients, so you may also see this written as:
Outliers Test
Q1 - 1.5 X IQR
Q3 + 1.5 X 1QR
Different types of sampling
SEE
Distribution of Box whisker diagram
see
How to calculate Q1 and Q3
For integration, how do you calculate the value of h
- H is the horizontal distance between each point
If x axis goes from 2, 3, 4, 5, 6
H = 1
Maximum areas of triangles
Split the error diff
ALSO
with the angles –> lower angle bounds for maximum and vice versa
Var(X)
Var(X) = np(1−p)
range of r
−1
domain
Simple random sampling
In this method, each individual in a population has an equal chance of being selected as part of the sample. A random number generator or a table of random numbers can be used to select the sample.
