In a study, 18 adults each look at two displays. 13 prefer display X, 2 prefer display Y and 3 have no preference. A sign test is used, with S as the number of the less frequent sign.
Which pair of values is correct?
[1 mark]The sign test
In a repeated measures study, the change in puzzle score for each of 14 adults after a training session was: +2, +1, 0, +4, −1, +3, +2, +1, 0, +5, −2, +1, +3, +2. The researcher used a sign test with a two-tailed hypothesis at the 0.05 level.
| N | 0.05 one-tailed (0.10 two-tailed) | 0.025 one-tailed (0.05 two-tailed) | 0.01 one-tailed (0.02 two-tailed) |
|---|---|---|---|
| 10 | 1 | 1 | 0 |
| 11 | 2 | 1 | 1 |
| 12 | 2 | 2 | 1 |
Part 1
Calculate the value of N.
[1 mark]Part 2
Calculate the value of S.
[1 mark]Part 3
Use the table of critical values to decide whether the result is significant. Explain your decision.
[3 marks]A teacher tests whether a revision app improves students' confidence. Twelve students rate their confidence from 1 to 10 before and after using the app for a month. The hypothesis is that confidence will be higher after using the app.
| Student | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Before | 4 | 5 | 6 | 3 | 7 | 5 | 4 | 6 | 5 | 2 | 6 | 5 |
| After | 6 | 7 | 6 | 5 | 6 | 8 | 4 | 8 | 7 | 5 | 7 | 4 |
Part 1
Calculate the value of S.
[2 marks]Part 2
Calculate the value of N.
[1 mark]Part 3
Critical values of S for : 0.05 one-tailed, 1; 0.025 one-tailed, 1; 0.01 one-tailed, 0. S must be equal to or less than the critical value to be significant. Which conclusion is correct at the 0.05 level?
[1 mark]In a taste test, 20 people try a new and an old recipe of the same soup. 14 prefer the new recipe, 4 prefer the old one and 2 have no preference. The hypothesis is that there will be a difference in preference between the recipes.
| N | 0.05 one-tailed (0.10 two-tailed) | 0.025 one-tailed (0.05 two-tailed) | 0.01 one-tailed (0.02 two-tailed) |
|---|---|---|---|
| 17 | 4 | 4 | 3 |
| 18 | 5 | 4 | 3 |
| 19 | 5 | 4 | 4 |
Part 1
Calculate the value of S.
[1 mark]Part 2
Explain whether the result is significant at the 0.05 level. Refer to the table in your answer.
[3 marks]A sign test on data from 15 participants (no ties) gives . The hypothesis was directional. Critical values of S for are: 0.05 one-tailed, 3; 0.025 one-tailed, 3; 0.01 one-tailed, 2.
Part 1
Which two statements are correct? Shade two boxes only.
[2 marks]Part 2
Explain why a researcher might choose to report the result at the 0.05 level rather than claim significance at a stricter level.
[2 marks]The sign test is one of the statistical tests in the A-level specification.
Explain two features of a study that would make the sign test the appropriate test to use.
[2 marks]