Chi-squared test for independence Problem set B Answers

1. (a) H0: the lunch a pupil chooses is independent of house. H1: the lunch a pupil chooses is not independent of house.
2. (b) df = 8

22.8

(a) 12; (b) 5; (c) 16

Expected: North: 18.9, 21.4, 19.7; South: 26.1, 29.6, 27.3. χ² = 11.2, p = 0.00363, df = 2

1. (a) 6.25
2. (b) 0.0280

1. (a) H0: book type is independent of age band. H1: book type is not independent of age band.
2. (b) df = 4
3. (c) χ² = 6.98, p = 0.137
4. (d) There is insufficient evidence, at the 5% significance level, that book type is not independent of age band.

1. (a) χ² = 12.2
2. (b) There is sufficient evidence, at the 5% significance level, that the size of an apple is not independent of the orchard.

1. (a) Tea: 24.2, 25.1, 19.4, 23.4; Coffee: 29.7, 30.8, 23.8, 28.7; Juice: 31.1, 32.1, 24.8, 30.0
2. (b) Tea, Weekly: 8.90
3. (c) Observed above expected: 40 against 25.1

1. (a) 26.2
2. (b) df = 1, χ² = 2.08. There is insufficient evidence, at the 5% significance level, that arriving late is not independent of eating breakfast.

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