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u52 It is important to note that the p-value is an observed random variable that will be dif- ferent for each random sample obtained for a statistical test. Thus, two different analysts could obtain their own random samples and sample means from a process population, and, thus, each would compute a different p-value. Example 9.1 Evaluating a New Production Process (Hypothesis Test) The production manager of Northern Windows, Inc. has asked you to evaluate a pro posed new procedure for producing its Regal line of double-hung windows. The pres ent process has a mean production of 80 units per hour with a population standard deviation of -8. The manager does not want to change to a new procedure unless there is strong evidence that the mean production level is higher with the new process Q1 6-3. Classify each of the following as either a Type l error or a Type Il error: (a) Putting an innocent person in jail (Type 1) (b) Releasing a guilty person from jail (Type II) (c) Eating (or not eating) a cookie that fell on the floor. (Type II) (d) Not eating a clean cookie (Type 1) (e) Not seeing a doctor as soon as possible after ingesting poison (Type II) 6-4. An automatic filling machine is used to fill 1-liter bottles of cola. The machine's output is approximately normal with a mean of 1.0 liter and a standard deviation of .01 liter. Output is monitored using means of samples of 25 observations, (a) Determine upper and lower control limits that will include roughly 97 percent of the sample means when the process is in control. (b) Given these sample means: 1.005, 1.001,998, 1.002, .995, and.999, is the process in control