Math AI: Hypothesis Testing (HL Part)

purpose of binomial hypothesis testing?

to figure out if an unusual result is just bad luck or evidence that something has actually changed

when to use binomial hypothesis testing?

• two outcomes (pass or fail)

• fixed number of trials

• mean and standard deviation are different

• constant probability

null hypothesis for binomial hypothesis testing?

Ho: p= po
e.g. both cheeses are equally likely to be selected so p=0.5

alternative hypothesis for binomial hypothesis testing?

H1: p is not equal to po
OR
p > po (null hypothesis probability)
OR
p < po (null hypothesis probability)

how to determine upper and lower bounds for binomial hypothesis testing?

if p > po, right tailed test, meaning lower bound is X.

if p < po, left tailed test, meaning upper bound is X.

conclusions for any test?

if p value is less than significance level, reject null hypothesis
if p value is more than significance level, fail to reject null hypothesis

purpose of poisson hypothesis testing?

to determine if the rate at which rare or independent events occur has significantly changed within a given interval of time or space

when to use poisson hypothesis testing?

• fixed time period

• many possible outcomes

• mean and variance is the same (parameter)

null hypothesis for poisson hypothesis testing?

Ho: data follows poisson distribution
OR
Ho: Po (value)

alternative hypothesis for poisson hypothesis testing?

H1: data does not follow poisson distribution

OR
H1: mean is less than Ho ( mean < Ho)

OR
H1: mean is more than Ho (mean > Ho)

if mean < Ho poisson hypothesis testing?

critical region is on the left
Lower bound: 0
upper bound: x

if mean > Ho poisson hypothesis testing?

critical region is on the right
lower bound: X
upper bound: 999999

What is PMCC?

Pearson Product Moment Correlation Coefficient test

purpose of PMCC test?

to test if there is a linear correlation for the whole population

null hypothesis for PMCC test?

Ho: p = 0 (population has no correlation)

alternative hypothesis for PMCC test?

H1: p is not equal to 0 (yes there is correlation)
OR
H1: p > 0 (positive correlation)
H1: p < 0 (negative correlation)

function on the calculator for PMCC test?

linear regression T-test to find PMCC for population (p val)

linear regression to find PMCC for sample ( r )