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Chapter 4: Q T4.2. (page 274)
You want to take a simple random sample (SRS) of of the students who live in a dormitory on campus. You label the students 001 to 816 in alphabetical order. In the table of random digits, you read the entries.
The first three students in your sample have labels
The correct option is (e)
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Go Blue! Michigan Stadium, also known as “The Big House,” seats over 100,000 fans for a football game. The University of Michigan athletic department plans to conduct a survey about concessions that are sold during games. Tickets are most expensive for seats near the field and on the sideline. The cheapest seats are high up in the end zones (where one of the authors sat as a student). A map of the stadium is shown.
(a) The athletic department is considering a stratified random sample. What would you recommend as the strata? Why?
(b) Explain why a cluster sample might be easier to obtain. What would you recommend for the clusters? Why?
In the cornfield An agriculture researcher wants to compare the yield of five corn varieties: A, B, C, D, and E. The field in which the experiment will be carried out increases in fertility from north to south. The researcher therefore divides the field into twenty five plots of equal size, arranged in five east–west rows of five plots each, as shown in the diagram.
(a) Explain why a randomized block design would be better than a completely randomized design in this setting.
(b) Should the researcher use the rows or the columns of the field as blocks? Justify your answer.
(c) Use technology or Table D to carry out the random assignment required by your design. Explain your method clearly.
Doctors and nurses Nurse-practitioners are nurses with advanced qualifications who often act much like primary-care physicians. Are they as effective as doctors at treating patients with chronic conditions? An experiment was conducted with patients who had been diagnosed with asthma, diabetes, or high blood pressure. Within each condition, patients were randomly assigned to either a doctor or a nurse-practitioner. The response variables included measures of the patients’ health and of their satisfaction with their medical care after six months.
(a) Which are the blocks in this experiment: the different diagnoses (asthma, etc.) or the type of care (nurse or doctor)? Why?
(b) Explain why a randomized block design is preferable to a completely randomized design in this setting.
Exercise and heart rate A student project measured the increase in the heart rates of fellow students when they stepped up and down for three minutes to the beat of a metronome. The step was either or inches high and the metronome beat was or steps per minute. Five students stepped at each combination of height and speed.
Treating prostate disease A large study used records from Canada’s national health care system to compare the effectiveness of two ways to treat prostate
disease. The two treatments are traditional surgery and a new method that does not require surgery. The records described many patients whose doctors had
chosen each method. The study found that patients treated by the new method were significantly more likely to die within eight years.
(a) Further study of the data showed that this conclusion was wrong. The extra deaths among patients who got the new method could be explained by lurking variables. What lurking variables might be confounded with a doctor’s choice of surgical or nonsurgical treatment?
(b) You have prostate patients who are willing to serve as subjects in an experiment to compare the two methods. Write a few sentences describing how you would design this experiment.
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