Sign test

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.

1. 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 .
2. State what other test might have been used, and give one advantage and one disadvantage this other test has over the sign test.

2 Part of Helen’s psychology dissertation involved the reaction times to a certain stimulus. She measured the reaction times of 30 randomly selected students, in seconds correct to 2 decimal places. The results are shown in the following stem-and-leaf diagram. Key: 18 | 3 means 1.83 seconds Helen wishes to test whether the population median time exceeds 1.80 seconds.

1. Give a reason why the Wilcoxon signed-rank test should not be used.
2. Carry out a suitable non-parametric test at the \(5 \%\) significance level.

1 Ten archers shot at targets with two types of bow. Their scores out of 100 are shown in the table.

1. Use the sign test, at the \(5 \%\) level of significance, to test the hypothesis that bow type \(P\) is better than bow type \(Q\).
2. Why would a Wilcoxon signed rank test, if valid, be a better test than the sign test?