5. (總分 15 分) Is a customer's preference for a cell phone affected by the age of the customer? If so, advertising might need to target a particular age group. Suppose a random sample of 500 customers aged 16 and older was selected, and their recent purchased cell phones along with their age groups were recorded, as shown in the table below. | Age Group | Apple | Sony | Asus | Other | |---|---|---|---|---| | 16-21 | 75 | 34 | 10 | 6 | | 21-30 | 89 | 42 | 19 | 10 | | 30-49 | 54 | 52 | 28 | 18 | | 50+ | 21 | 25 | 7 | 10 |

4. (總分 40 分) A statistics instructor is interested in applying a simple regression to test whether students' performance in the midterm exam (x, midterm exam scores) is associated with their performance in the final exam (y, final exam scores). The model to be estimated is y = a + βx, and the data is as follows: | Student | Midterm exam scores | Final exam scores | Student | Midterm exam scores | Final exam scores | |---|---|---|---|---|---| | 1 | 100 | 98 | 11 | 88 | 84 | | 2 | 96 | 97 | 12 | 92 | 93 | | 3 | 88 | 88 | 13 | 68 | 57 | | 4 | 100 | 100 | 14 | 84 | 84 | | 5 | 100 | 100 | 15 | 84 | 81 | | 6 | 96 | 78 | 16 | 88 | 83 | | 7 | 80 | 68 | 17 | 72 | 84 | | 8 | 68 | 47 | 18 | 88 | 93 | | 9 | 92 | 90 | 19 | 72 | 57 | | 10 | 96 | 94 | 20 | 88 | 83 |