Type I errors Problem set B Answers

1. (a) 0.01
2. (b) 0.06

1. (a) 0.110
2. (b) 0.0455

1. (a) 0.0411
2. (b) 0.0467

1. (a) 0.0674
2. (b) 0.0172

1. (a) X ≥ 8
2. (b) 0.0221

1. (a) X ≤ 7
2. (b) 0.0316

0.0691

1. (a) The colleague decides that the mean time has changed when it is in fact still 25 minutes.
2. (b) 0.01

1. (a) X ≥ 7
2. (b) 0.0258
3. (c) X takes whole numbers only, so the probabilities of the critical regions jump. No region has probability exactly 0.05, and we take the largest one that does not exceed it.

1. (a) 0.115
2. (b) 0.00820
3. (c) With the same critical value, a larger sample has a smaller standard deviation of the mean, so the probability of a Type I error is smaller.