Chi-squared goodness of fit Problem set B Answers

\(H_0\): preferences are in the proportions 1/2, 1/3, 1/6. \(H_1\): they are not.

1. (a) 11
2. (b) 5
3. (c) 7

90, 70, 50, 40

24

1. (a) df = 4; E = 30
2. (b) χ² = 4.07, p = 0.397

1. (a) \(H_0\): the sales are in the stated proportions; \(H_1\): they are not
2. (b) df = 3; E = 135, 75, 60, 30
3. (c) χ² = 3.83, p = 0.28
4. (d) Do not reject \(H_0\). Insufficient evidence, at the 5% level, that the sales differ from the stated proportions.

1. (a) \(H_0\): equally popular; \(H_1\): not equally popular; E = 60
2. (b) χ² = 9.63
3. (c) 9.63 > 7.815: reject \(H_0\). Sufficient evidence that the room types are not equally popular

1. (a) 25
2. (b) Yes: every count is within 3 of 25

1. (a) χ² = 15.8, p = 0.00323, df = 4
2. (b) Reject \(H_0\): sufficient evidence that absences are not equally likely on each day
3. (c) Monday has far more absences, for example students stay at home after a weekend

1. (a) χ² = 0.04, p = 0.998
2. (b) They are very close to the expected frequencies
3. (c) The results fit equal probabilities almost perfectly, closer than real spins usually are. The student may have made up some of the results