4 The levels of impurity in a particular alloy were measured using a random sample of 20 specimens. The results, in suitable units, were as follows.
| 3.00 | 2.05 | 3.15 | 2.65 | 3.50 | 3.25 | 2.85 | 3.35 | 2.65 | 2.75 |
| 2.90 | 2.20 | 2.95 | 3.05 | 3.65 | 3.45 | 2.55 | 2.15 | 2.80 | 2.60 |
- Use the sign test, at the \(5 \%\) significance level, to decide if there is evidence that the population median level of impurity is greater than 2.70 .
- State what other test might have been used, and give one advantage and one disadvantage this other test has over the sign test.