It is believed that all crisp flavours are equally liked. A survey is conducted in which 100 people are asked for their favourite crisp flavour, the results of which are shown in the following table: Flavour 2 3 A 5 6 Preferred 15 18 20 16 14 17 (a) State which test you should use to determine whether each flavour is equally liked. (2 marks) (b) State the null hypothesis and the alternative hypothesis for this test. (1 marks) (c) Assuming the null hypothesis, calculate the expected frequencies. (2 marks) (d) Find the test statistic. Should we reject or accept the null hypothesis at the 5% significance level? (3 marks) The survey also asked for whether or not the participants were vegetarian. The table below shows this data with vegetarians and non-vegetarians separated. Flavour 2 3 A 5 6 Vegetarian 7 6 9 5 7 Non-vegetarian 8 12 11 B 10 (e) Form a table showing expected frequencies for each combination of flavour and vegetarianon-vegetarian, assuming that favourite flavour and being vegetarian are independent. (4 marks) (f) Perform a test at the 5% significance level to determine if being a vegetarian is independent of favourite crisp flavour. (8 marks)