Question 28 (20 marks) Buying a new laptop can be an overwhelming experience, with so many technical features and specications to consider along battery life. After searching on the Internet, you consider two brands: Apple and Orange. a) Suppose that you can randomly sample 20 of 100 laptops from an Apple store and nd the sample mean battery life is 779 minutes and the standard deviation is 42 minutes. Construct 95% condence intervals for the true mean of the battery life of Apple laptops. [7 marks] b) Suppose that you can also randomly sample 20 of 80 laptops from another store, Orange, and nd the sample mean battery life is 812 minutes and the standard deviation is 109 minutes. Construct 95% condence intervals for the true mean for the battery life of Orange laptops. [7 marks] c) Based on the condence intervals found in part a) and b), what brand should you buy if you think battery life is the most important feature of your laptop? Explain your decision. Are there any points of concern that should be taken into account when you make the decision? [2+2+2=6 marks] [Total Marks for Question 28 - 20 marks] Question 29 Instant noodles are a popular convenience food eaten all over the world and Magic Beef noodles is the most popular brand. Nutrition facts displaced on a package of Magic Beef noodles indicate that one serving size package contains 99 of fat. An inspector collects 5 random packages which follow a normal distribution, and reports the amount of fat (g/package) as follows: m a) Based on the above observations, determine whether the nutrition facts reported by Magic Beef is accurate with the level of signicance 0 = 5%. [7 marks] b) To solidify the conclusion, 5 additional packages are tested, and the amount of fat found from these additional packages are: \"-9.5\" Based on the total of 10 observations, is there evidence that a package of Magic Beef noodles contains more than 99 of fat? [7 marks] c) Based on the 10 observations above, construct the 95% condence intervals for the average amount of fat containing in a package of Magic Beef noodles. 1-; .l 1