Contingency tables and the chi-squared testAQA A-Level Further Maths: Mind map

Exam questions on Contingency tables and the chi-squared test

1. A survey of 150 employees records how they travel to work and whether they live in town. Of the 40 who walk, 30 live in town. Of the 60 who take the bus, 25 live in town. Of the 50 who drive, 15 live in town. A chi-squared test for association is to be carried out.
   State the null hypothesis and the number of degrees of freedom for the test.2 marks
2. Hospital records for 200 patients from three wards, A, B and C, give each patient's recovery outcome. Ward A has 70 patients: 48 recovered fully, 20 partially and 2 not at all. Ward B has 60 patients: 35 fully, 22 partially and 3 not at all. Ward C has 70 patients: 27 fully, 36 partially and 7 not at all.
   Explain why two of the outcome categories must be combined before the test is carried out, and state the degrees of freedom after doing so.2 marks
3. A cafe owner records the drink chosen by 120 customers: 60 in the morning and 60 in the afternoon. In the morning, 18 chose tea, 30 chose coffee and 12 chose juice. In the afternoon, 24 chose tea, 14 chose coffee and 22 chose juice.
   Find the expected frequency for each cell, assuming the drink is independent of the time of day, and calculate the value of the test statistic $\sum\frac{(O-E)^2}{E}$.3 marks