Chi-squared Test

to find the expected frequency of each element in the table, find the two product of the two relevant probability and times by the total number of sample

If the expected frequency found is less than 5, then need to add to the next column to combine the data

This then can be used to calculate the chi-square statistic

Then use the formula booklet to find the corrosponding statistic value depending on the significance level, compare this with the calculated value, if calculated value is higher, then there is sufficient evidence to reject H0

Hypothesis testing (always one tailed test):

• H0: the two variables are independent

• H1: the two variables are not independent

• or

• H0: distribution is a good fit

• H1: distribution is not a good fit

In a contingency table, the degree of freedom is always (m-1)(n-1)

But if not in a table, degree of freedom always minus one from the number of data, unless we estimated the value of mean or anything when finding the test statistics, then we minus another 1.

Note: In questions when asking whether a distribution is a good find, to find the mean, use expectation formula, then to find the expected frequency need to put in the data into the distributions to find probability then times by the frequency, think of expected frequency in this case the frequency if distribution is a good fit

degree of freedom needs to minus one if mean is calculated as this is an estimate

If test statistics contribution is higher, this means the data is more unexpected, so mention whether the observed frequency is more or less than the expected

if test statistics contribution is low, this means data does not contribute much to the test statistics