Chi-squared test for independence Problem set A Answers

1. (a) H0: the way a student travels to school is independent of year group. H1: the way a student travels to school is not independent of year group.
2. (b) df = 6

27.4

(a) 8; (b) 5; (c) 9

Expected: Girls: 31.1, 30.6, 23.3; Boys: 32.9, 32.4, 24.7. χ² = 11.0, p = 0.00401, df = 2

1. (a) 11.1
2. (b) 0.0297

1. (a) H0: holiday type is independent of age group. H1: holiday type is not independent of age group.
2. (b) df = 4
3. (c) χ² = 8.63, p = 0.0711
4. (d) There is insufficient evidence, at the 5% significance level, that holiday type is not independent of age group.

1. (a) χ² = 9.94
2. (b) There is sufficient evidence, at the 5% significance level, that the case chosen is not independent of the colour chosen.

1. (a) Basic: 27.5, 24.3, 22.6, 20.6; Standard: 34.2, 30.2, 28.1, 25.5; Premium: 33.3, 29.5, 27.3, 24.9
2. (b) Basic, 1 day: 15.3
3. (c) Observed above expected: 48 against 27.5

1. (a) 21.5
2. (b) df = 1, χ² = 1.11. There is insufficient evidence, at the 5% significance level, that catching a cold is not independent of taking the vitamin.

1. (a) reject H0 at 5%
2. (b) do not reject H0 at 1%