A company that manufactures brackets for an automaker regularly selects brackets from the production line and performs a torque test. The goal is for mean torque to equal 125. Let X equal the torque and assume that X is (#, 02). We shall use a sample of size n = 15 to test Ho: J = 125 against a two-sided alternative hypothesis. (a) Give the test statistic and a critical region with significance level a = 0.05. Sketch a figure illustrating the critical region. (b) Use the following observations to calculate the value of the test statistic and state your conclusion: 128 149 136 114 126 142 124 136 122 118 122 129 118 122 129 The ornamental ground cover Vinca minor is spreading rapidly through the Hope College Biology Field Station because it can out compete the small, native woody vegetation. In an attempt to discover whether Vinca minor utilized natural chemical weapons to inhibit the growth of the native vegetation, Hope biology students conducted an experiment in which they treated 33 sunflower seedlings with extracts taken from Vinca minor roots for several weeks and then measured the heights of the seedlings. Let X equal the height of one of these seedlings and assume that the distribution of X is /(, of). The observed growths (in cm) were 11.5 11.8 15.7 16.1 14.1 10.5 15.2 19.0 12.8 12.4 19.2 13.5 16.5 13.5 14.4 16.7 10.9 13.0 15.1 17.1 13.3 12.4 8.5 14.3 12.9 11.1 15.0 13.3 15.8 13.5 9.3 12.2 10.3 The students also planted some control sunflower seedlings that had a mean height of 15.7 cm.We shall test the null hypothesis Ho: / = 15.7 against the alternative hypothesis Hip