In this question we will formulate a measure to quantify the level of association between the two categorical variables Such a measure is often used in a statistical test called Chi square test for assessing whether there is an association between two categorical variables This question is also used to motivate the learning of independence and to connect the concept back to what we have learnt in the course Let s revisit the example we have looked at in the course How is diet type high cholesterol diet versus low cholesterol diet related to the risk of coronary heart disease Data of 23 individuals High cholesterol diet Low cholesterol diet From the table we find that the probability of having heart disease is 13 23 and the probability of having high cholesterol diet is 15 23 Similarly we can find the probability of not having heart disease and the probability of having low cholesterol diet Heart disease No heart disease Total i 11 iii 4 15 ii 2 iv 6 8 13 10 23 Part a If there is no association between the two variables i e the two are independent the probability of having heart disease and high cholesterol diet is Round to four decimal places 0 4783 Part b If the two variables are independent we should expect the number of individuals with heart disease and high cholestoral diet to be the probability in Part a multiplied by 23 individuals which is Round to two decimal places 0 37 Part c Repeating Part b we find that the expected number of individuals for the cells ii iii iv respectively on the table are 4 52 6 52 3 48 The following measure called Chi square test statistic x Observed Expected Expected