( a) A manufacturer of olive oil uses machines to dispense olive oil into bottles that move along a filling line. The machine that dispenses olive oil is working properly when 750 ml is dispensed. Suppose that the average amount dispensed in a particular sample of 25 bottles is 748 ml with a variance of 9. Manufacture wants to know whether there is any statistical evidence to stop the operating of the dispensing machine for repairs.

(i) Write null and alternative hypotheses. (ii) Is this a one-tail or two-tail test?(iii) Perform a suitable hypothesis test and write your conclusion.(Use 1% significance level). (iv) Is this conclusion valid at 5% significance level? (Justify your answer without using any statistical table). (v) State the assumption under the above test.

( b) A researcher was interested in the population proportion of adults who are worried a lot about the children's addiction to online games. Survey results show that sixty percent of 50 adults worried about the children's addiction to online games. Construct a 95% confidence interval for the population proportion of adults who are worried a lot about the children's addiction to online games and interpret the results