please help with 2,4

Problem 2 You're developing a foam insulation product that expands after application. You want the final (after expansion} height of the insulation to be more than 175 mm. You performed an experiment of spraying the insulation on 10 different surfaces (in a similar manner on similar surfaces), and you recorded the following insulation heights. 171.9 186.2 195.6 164.6 147.8 155.4 191.5 201.2 171.4 201.1 a. Is there sufficient evidence to conclude that your condition is met? Use the critical value approach with signicance of 0.1. b. Find the probability of type II error if the true mean height is 185 mm. c. Find the probability of type II error if the true mean height is 195 mm. d. Discuss how and why the probability of type II error changes. Problem 3 You're a healthcare engineering consultant and you're analyzing the emergency room design at Pawhuska Hospital, Inc. In homework 8.xlsx you'll nd sample data for the waiting time (in minutes) of non-critical patients entering the emergency room. You have reason to believe that the standard deviation of non-critical patient waiting time is more than 20 minutes. Test that belief with the p-value approach using Excel. Problem 4 In the manufacture of machinery, it is essential to utilize parts that conform to specifications. In the past, diameters of the ball bearings produced back at Kruger Industrial Smoothing had a variance of 0.00156 mmz. To cut costs, you as a quality engineer instituted a less expensive production method. The diameters (in mm) of a sample of 50 ball bearings collected after the new production method are found in the Homework 8.xlsx le. 00 the data provide sufcient evidence to indicate that diameters of ball bearings produced by the new process are more variable than those produced by the old process? Test at a: = 0.05. a. Use the p-value approach using the tables in the book. b. Use the p-value approach using Excel. Problem 5 You're a quality control engineer for Norman's fourth largest cracker factory, and you plan to implement some process changes if you conclude that the mean weight of a 32 ounce box of saltine crackers is less than 32 ounces. Based on a sample of 15 boxes, you found an average and standard deviation of cracker box weight of 31.6 ounces and 1.2 ounces, respectively. a. Draw conclusions with the critical value approach at 99% condence. b. What is the probability that you conclude that no process changes are needed when the actual mean box weight is 31.7 ounces? Use the table in the textbook. c. Redo part b, but instead use Excel