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

1. (a) \(\bar X < 62.4\)
2. (b) \(\bar X < 2.28\)

1. (a) \(\bar X > 125\)
2. (b) \(\bar X > 0.896\)

1. (a) \(\bar X < 33.0\) and \(\bar X > 37.0\)
2. (b) \(\bar X < 207\) and \(\bar X > 213\)

1. (a) H0: μ = 340, H1: μ < 340
2. (b) \(\bar X < 338\)
3. (c) Reject H0: sufficient evidence that the mean has decreased.

1. (a) \(\bar X > 34.3\)
2. (b) Reject H0: sufficient evidence that the mean has increased.

1. (a) \(\bar X < 467\) and \(\bar X > 473\)
2. (b) Reject H0: sufficient evidence that the mean has changed.

1. (a) \(\bar X < 784\)
2. (b) \(\bar X < 792\)
3. (c) The critical value moves closer to 800. A larger sample has a smaller standard deviation of the mean, so a smaller departure from 800 is enough to reject H0.

0.0228 (about 2.28%)