Chisquare goodness of fit test  Hypothesis Testing
Chisquare goodness of fit test
Lessons
Notes:
The chisquare distribution is the sum of standard normal distribution(s) squared. The degrees of freedom for a chisquare distribution is how many standard normal distribution(s) squared you are summing.
Normal distribution:
$X\sim N (\mu, \sigma^2)=$ Normal Distribution with mean ‘$\mu$’ and standard deviation ‘$\sigma$’
So ChiSquare Distribution with k degrees of freedom:
$X^2=N_1(0,1)^2+N_2(0,1)^2+\cdots+N_k(0,1)^2$
Hypothesis Testing
ChiSquare distribution hypothesis testing comes in handy for seeing whether the observed value of some experiment fit the expected values.
$O_i$: the $i^{th}$ observed data point
$E_i$: the $i^{th}$ estimated data point
TestStatistic:
$X^2=\frac{(O_1E_1)}{E_1}+\frac{(O_2E_2)}{E_2}+\cdots+\frac{(O_nE_n)}{E_n}$
The critical value is found by looking at the Chi Distribution table

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