Combining categories in a chi-squared test Problem set B Answers

1. (a) 21.0
2. (b) Electric, 3 to 8 years: 3.73; Electric, Over 8 years: 3.93

1. (a) Year 7, 4 to 6 h: 4.75; Year 7, Over 6 h: 4.47; Year 9, Over 6 h: 4.83
2. (b) Over 4 h = 4 to 6 h + Over 6 h. New table: Year 7: 31, 10, 9; Year 8: 45, 18, 12; Year 9: 29, 13, 12
3. (c) df = 4

χ² = 7.99, df = 2, p = 0.0184: reject H0

χ² = 11.0, df = 4, p = 0.0266: reject H0

χ² = 4.60, df = 4, p = 0.331: do not reject H0

χ² = 2.25, df = 2, p = 0.324: do not reject H0

1. (a) New table has an expected frequency of 2.20, which is not greater than 5
2. (b) χ² = 0.997, df = 2, p = 0.607: do not reject H0

1. (a) χ² = 8.01, df = 2, p = 0.0182: reject H0
2. (b) p = 0.0182 > 0.01, so do not reject H0 at 1%. The p-value is between 0.01 and 0.05.