Essential Statistics Completely Randomized Name: __________________________________
1 A chemist wishes to test the effect of four chemical agents on the tensile strength of a particular type of cloth, measured in grams per denier (gpd). The raw cloth is delivered in bolts, and one expects significant tensile strength variability between bolts. What type of experimental design should be used? If 24 samples of each treatment will be taken, but each bolt only supplies 12 samples total, then how should the experiment be designed in order to eliminate the effect of bolt variability?
2 A medical study of heart surgery investigates the effect of a drug called a beta-blocker on the pulse rate of the patient during surgery. The pulse rate will be measured at a specific point during the operation. The investigators will use 20 patients facing heart surgery as subjects. You have a list of these patients, numbered 1 to 20, in alphabetical order. a.
Describe the design of a completely randomized experiment to test the effect of beta-blockers on pulse rate during surgery. Write a few sentences about how you would implement your design. b.
Use the section from the random digits table below to carry out the randomization required by your design and report the result.
3 Canada requires that cars be equipped with “day time running lights,” headlights that automatically come on at a low level when the car is started. Some manufacturers are not equipping cars old in the Unites States with running lights Will running lights reduce accidents by making cars more visible? a) Briefly describe the design of the experiment to help answer this question. In particular, what response variable will you examine? b) What cautions would you draw that apply to an experiment on the effects of running lights?
4 Substances that case cancer should not appear in our food. We don’t want to experiment on people to learn what substances cause cancer, so we experiment on rats instead. The rats are specially bred to have more tumors than humans do. They are fed large doses of the test chemical for most of their natural lives, about two years. Briefly address the questions that arise in using these experimental design aspects to decide what is safe for a human.
5 The National Institute of Health is at last sponsoring proper clinic trials of some natural remedies. In one study at Duke University, 330 patients with mild depression are enrolled in a trial to compare St John’s Wort with a placebo and with Xoloft, a common prescription drug for depression. The Beck depression Inventory is common instrument that rate the severity of depression on a 0 to 3 scale. a) What would you use as a response variable to measure change in depression after treatment? b) Outline the design of a completely randomized clinical trial for this study. c) What other precautions would you take in this trial?