Question 5 (i) Explain clearly what you understand by: (a) Type I Error; (b) Type II Error in the context of hypothesis testing. Explain the relevance of these errors in hypothesis testing. [8 marks] (ii) X is a random variable normally distributed with mean u and variance 02. Write down a 95%% confidence interval for u based on 100 independent observations on X for a specified value of 62. How do you interpret this interval? If the sample size is doubled, what effect will it have on the length of the interval? [8 marks] (iii) A certified public account plans to audit the financial records of a company to estimate the proportion of account ledger pages which are in error. The accountant believes that the ledger page error rate is in the neighbourhood of 1% and wishes to estimate the true rate correct to within 0.5%. How many ledger pages should be included in the sample? If, moreover, the accountant has no prior idea of the error rate, how many ledger pages should then be included in the sample? [8 marks] (iv) The Agricultural Research Institute would like to evaluate the impact of two insecticides Pert and Acti on tomato plants. A monitor of the use of the insecticides on two plots of land gives the following results: Insecticide No. of tomato No. of infected plants tomato plants Per 400 24 Acti 300 30 Are the two insecticides equally effective? [9 marks]