(b) The mean productivity index for the operators in a factory used to be 25. At the beginning of last year, a random sample of 25 operators was selected to undergo training on a new production technique. After the training it was found that the sample mean productivity index was 27 and the sample standard deviation was 5. {i} Test the hypothesis at signicance level of 0.05 whether the new production technique was effective in improving the mean productivity index. (10 marks) {ii} At 0.025 level of significance, investigate whether the claim in {i}