(Solved): (Adapted from Textbook 27.2) The Cleveland Casting Plant is a large highly automated producer of gr ...

(Adapted from Textbook 27.2) The Cleveland Casting Plant is a large highly automated producer of gray and nodular iron automotive castings for Ford Motor Company. One process variable of interest to Cleveland Casting is the pouring temperature of molten iron. The pouring temperatures (in degrees Fahrenheit) of ten crankshafts are given in Table 27.4. The target setting for the pouring temperature is set at 2550 degrees. One wants to conduct a test at level $?=0.01$ to determine whether the pouring temperature differs from the target setting. You are given the following ten data points for pouring temperatures: (a) Compute the sample mean and verify that the sample variance is approximately 517.34 . (b) Formulate an appropriate null hypothesis and alternative hypothesis. (c) Assume that the data is normally distributed. Formulate a decision rule for testing at level $?=0.01$. You should compare this part to what we've done with the normal distribution; however, you'll need to identify the right distribution for this setting! (d) For the given data: should you reject the null hypothesis at this level? (e) With your decision rule: what is the probability of making a type II error if the acutal pouring temperature has mean 2530 ?