11. A factory produces paper which is expected to have a mean length of 11 inches. The standard deviation is known to be 0.2 inches. An employee says she thinks something may have gone wrong with the machine and she suspects it is now producing paper of a different length. A random sample of 100 pages is taken and the mean paper length is 10.998 inches. (a) Construct a 95 per cent confidence interval for the population mean paper length. (5 marks) (b) What does this suggest about the machine? (1 mark) (c) If you had not known the standard deviation, how would you have answered the question? (2 marks) (d) If you wanted a confidence interval that was only half as wide, what sample size would be required? (2 marks) 11. A factory produces paper which is expected to have a mean length of 11 inches. The standard deviation is known to be 0.2 inches. An employee says she thinks something may have gone wrong with the machine and she suspects it is now producing paper of a different length. A random sample of 100 pages is taken and the mean paper length is 10.998 inches. (a) Construct a 95 per cent confidence interval for the population mean paper length. (5 marks) (b) What does this suggest about the machine? (1 mark) (c) If you had not known the standard deviation, how would you have answered the question? (2 marks) (d) If you wanted a confidence interval that was only half as wide, what sample size would be required? (2 marks)