Ql(a) The following contingency table shows the annual salary of 300 respondents. Age Group Annual Salary (RM '000) Below 30 (L) 30-70 (M) Above 70 (HD) Below 30 (B) 51 27 22 30-40 (C) 29 46 35 Above (A) 20 30 40 (i) Show whether there is any evidence of a significant association between age group and annual salary. Use a = 0.01. (10 marks) (ii) Construct a 99% confidence interval for the true proportion of respondents with annual salary above RM70000. Thus, interpret the answer. (5 marks) (iii) It is claimed that the proportion of respondents who are below 30 years old and earn above RM 70000 is 8%. Can the claim be supported at 2% level of significance? (10 marks) (b) An intelligence test has been given to the primary school students for several years and it is assumed that the scores are normally distributed with an average of 85. A group of 50 primary school students obtained a mean grade of 84 and a standard deviation of 5 in the test this year. Is this batch students inferior in intelligence to the past years' primary school students using 2% level of significance? (10 marks) (i) A mechanic claims that one particular brand of car batteries can last at least 700 days and a standard deviation of 20 days. A simple random sample of 30 of the car batteries is taken and the mean life is found to be 680 days. Test the mechanic claim at 1.5% level of significance. (10 marks) (ii) Find a 98% confidence interval estimate for the mean life of all the car batteries of this particular brand