Question 4 (Total: 25 marks) (a) The bottling machines of a company fill up cans with cherry soda drink to a volume of about 350 ml. It is noted that the volume in each can of soda follows a normal distribution. To test the consistency of the machines, 20 cans are randomly selected and the mean volume is 355 m/ while the standard deviation is 16 ml. (1) What is the 95% confidence interval for the average volume of the selected cans? (6 marks) (1) With reference to this context, explain the meaning of the confidence interval that you have obtained. (6 marks) (b) A company claims that the standby time for its new model of mobile phone is at least 46 hours. A sample of 20 phones yielded a mean standby time of 44 hours and standard deviation of 2.8 hours. It is assumed that the standby time is normally distributed. Conduct a hypothesis testing using the critical value approach, at the 0.05 level of significance. Is there evidence that the mean standby time as claimed by the company is true? (13 marks)