1. For a sample of 35 items from a population for which the standard deviation is C 5 20.5, the sample mean is 458.0. At the 0.05 level of significance, test H0: µ 5 450 versus H1: µ =! 450. Determine and interpret the p-value for the test.
2. For a sample of 12 items from a normally dis- tributed population for which the standard deviation is C 5 17.0, the sample mean is 230.8. At the 0.05 level of significance, test H0: µ # 220 versus H1: µ . 220. Determine and interpret the p-value for the test.
3. A quality-assurance inspector periodically examines the output of a machine to determine whether it is properly adjusted. When set properly, the machine pro- duces nails having a mean length of 2.000 inches, with a standard deviation of 0.070 inches. For a sample of 35 nails, the mean length is 2.025 inches. Using the 0.01 level of significance, examine the null hypothesis that the machine is adjusted properly. Determine and interpret the p-value for the test.