Paper 3

X̄ vs μ

Mu - Population mean

X bar - sample mean

Distribution of the mean of X

X̄ ~ N(μ, σ² / n)

P( A | B )

P(AnB) / P(B)

Φ(a) → “phi”

Alternate way of writing P(Z<a)

Standardised

What does n and r mean in nCr

nCr is number of ways to select r items

n is number of items in a list, r is number of items selected from the list

Binomial note

Dont forget P(X<0) is perfectly valid, and doesn’t necessary equal 0 or 1

p-value

Not given probability but your calculated probability.

For two-tailed tests, multiply this number by 2

When is binomial model appropriate

• fixed number of trials

• trials are independent

• two possible outcomes for each trial

When are normal approximations appropriate

• Probability is close to 0.5

• n is large

Dont forget the continuity correction!!!

CAMBORNE

Camborne, UK

NOT Canberra, Australia. Perth is in Australia

Quartiles for discrete data

Same logic as finding the median for data of 2k items or 2k+1 items:

if n/4 is a whole number, use n/4 + 0.5 → this isn’t the value, but the position of the value

if n/4 is a decimal, round up (always up) → this isn’t the value, but the position of the value

Interpolation assumption

Data in each class is evenly spread