14 4. Charlie carried out a survey on the main type of investment people have. The contingency table below shows the results of a survey of a random sample of people. Main type of investment Bonds Cash Stocks Age 25 – 44 a b − e e 45 – 75 c d − 59 59 (a) Find an expression, in terms of a, b, c and d, for the difference between the observed and the expected value (O − E ) for the group whose main type of investment is Bonds and are aged 45 – 75 Express your answer as a single fraction in its simplest form. (4) Given that O E E − ( ) ∑ 2 = 9.62 for this information, (b) test, at the 5% level of significance, whether or not there is evidence of an association between the age of a person and the main type of investment they have. You should state your hypotheses, critical value and conclusion clearly. You may assume that no cells need to be combined. (3) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________