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

1. (a) 1.82
2. (b) Stalls, Under 16: 1.82; Circle, Under 16: 4.24; Balcony, Under 16: 1.95

1. (a) Under 3.5 h, Under 25: 4.17; 3.5 to 4.5 h, Under 25: 3.51; Over 4.5 h, Under 25: 3.32
2. (b) Under 35 = Under 25 + 25 to 34. New table: Under 3.5 h: 12, 39, 18; 3.5 to 4.5 h: 7, 44, 7; Over 4.5 h: 9, 37, 9
3. (c) df = 4

χ² = 8.16, df = 2, p = 0.0169: reject H0

χ² = 10.5, df = 4, p = 0.0327: reject H0

χ² = 1.96, df = 4, p = 0.743: do not reject H0

χ² = 0.133, df = 2, p = 0.936: do not reject H0

1. (a) New table has an expected frequency of 3.00, which is not greater than 5
2. (b) χ² = 1.01, df = 2, p = 0.603: 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.