Critical regions for a test of a mean Problem set B Answers

1. (a) \(\bar X < 17.8\)
2. (b) \(\bar X < 0.599\)

1. (a) \(\bar X > 75.5\)
2. (b) \(\bar X > 4.35\)

1. (a) \(\bar X < 17.2\) and \(\bar X > 18.8\)
2. (b) \(\bar X < 0.929\) and \(\bar X > 0.971\)

1. (a) H0: μ = 54, H1: μ < 54
2. (b) \(\bar X < 52.6\)
3. (c) Do not reject H0: insufficient evidence that the mean has decreased.

1. (a) \(\bar X > 84.9\)
2. (b) Do not reject H0: insufficient evidence that the mean has increased.

1. (a) \(\bar X < 24.2\) and \(\bar X > 25.8\)
2. (b) Do not reject H0: insufficient evidence that the mean has changed.

1. (a) \(\bar X < 50.3\)
2. (b) \(\bar X < 52.7\)
3. (c) The critical value moves closer to 55. A larger sample has a smaller standard deviation of the mean, so a smaller departure from 55 is enough to reject H0.

0.0668 (about 6.68%)