probability, hypothesis testing stats key definitions

https://www.mathsbox.org.uk/alevel/revision/rrevision/astat.pdf

Independent events

P(A∩B) = P(A) x P(B)

mutually exclusive events

P(A∩B) = 0

P(A∪B) =P(A) + P(B)

conditional probability

When the outcome of the first event effects the outcome of a second event the probability of the second event happening is conditional on the probability of the first event happening.

P(B|A) means that the probability of B given that A has occurred

P(B|A) = 𝑃(𝐴∩𝐵)/P(A)

critical value

the first value within the critical region that means you reject the H0 (null hypothesis)

critical region

the set of values that lead to you rejecting the H0

Acceptance region

the set of values that lead to you accepting the H0

significance level

the probability of rejecting the null hypothesis when it is true

formula for the Z value in normal distribution

Z = X - μ / σ

σ = standard deviation

μ = mean

standard normal distribution

Z ~N(0,1)

μ = 0

σ = 1

Binomial distribution

X~ B(n,p)

n= number of trials

p = probability of success

normal distribution

X~N(𝜇, 𝜎²)

Reject H0

p<a the probability is smaller than the sig level

“There is sufficient evidence to suggest that ………is underestimation/overestimating…….”

Accept H0

p>a. probability is bigger than the sig level

“There is insufficient evidence to suggest that ……increase/decrease……therefore we cannot reject the null hypothesis that p = a.”