1. EXTRA PRACTICE WITH ANSWERS
CHAPTER 4
EXTRA PRACTICE WITH ANSWERS

2. 1. Read the following article about the connection between vitamin E and heart bypass surgery. Vitamin E may have special health benefits Large doses of vitamin E apparently can reduce harmful side effects of bypass surgery in heart patients. A study involving 28 bypass patients found that the 14 randomly-assigned patients who took vitamin E for two weeks before their operations had significantly better heart function after the procedure than the 14 randomly- assigned patients who took placebos. The vitamins apparently prevent damage to the heart muscle by destroying the toxic chemicals, called free radicals, that form when blood is cut off during the surgery, said Dr. Terrance Yau of the University of Toronto.

3. a) Explain why this is an experiment and not an observational study.
This is an experiment because treatments (vitamin E, placebo) are imposed on the subjects.
b) Identify the explanatory and response variables.
Explanatory variable: Vitamin E treatment; Response: heart function.
c) Identify the type of experimental design used in this study. Justify your answer.
Completely randomized design. Each subject is assigned to one of the two groups randomly.

4. d) In the second sentence above is the phrase, “…the 14 patients who took vitamin E for two weeks before their operations had significantly better heart function after the procedure …” What is the statistical meaning of the word “significantly” in the context of this study? Significantly means that the difference found in the heart function between subjects in the two treatments was large enough that it was unlikely to have arisen from chance variation. e) This was a controlled experiment. Describe how it was controlled and explain the purpose of doing so. Comparing subjects who were given vitamin E to others who were given a placebo (the controls) allowed the researchers to isolate the impact of vitamin E from any other variables.

5. 2. As a researcher for a pharmaceutical company, you are designing a study to test the effectiveness of a new treatment for migraine headaches. You have been given a list of 126 people willing to participate in the trial. The first 70 people are female; the remaining 56 are male.
a) Preliminary research suggests that men and women respond differently to this new treatment. What sort of experimental design would you choose for this study, and why?
A randomized block design—blocking by gender—will reduce the impact that differences between the responses of men and women to the treatment might have on variability arising from random assignment.

6. b) Explain why an experiment involving 70 women and 56 men is preferable to one involving 10 women and 8 men. A larger number of subjects—greater replication—decreases the impact of random variation on experimental results, thereby increasing our ability to distinguish the effects of the treatment.

7. c) Describe a design for this experiment
c) Describe a design for this experiment. Be sure to include a description of how you assign individuals to the treatment groups.
First create two blocks comprised of the 70 women and the 56 men. Then, within each block assign the women numbers from 01 to 70 and the men numbers from 01 to 56. Choose 2-digit numbers from the random number table, ignoring repeats and unassigned
numbers, until you have selected 35 women. Then begin elsewhere in the table and follow the same procedure to randomly select 28 men. These subjects will be given the new migraine treatment, and the remaining subjects will receive a commonly-used standard treatment. Compare relief from migraine pain between the treatment group and the control group. OR

8. First create two blocks comprised of the 70 women and the 56 men
First create two blocks comprised of the 70 women and the 56 men. Write the women’s names on 70 identical slips of paper, place the slips in a hat, and mix them well. Pull out 35 slips to determine which women will be given the new migraine treatment and the remaining 35 subjects will receive a commonly-used standard treatment. Randomly assign the 56 men into two groups of 28 using a similar process. Compare relief from migraine pain between the treatment group and the control group.

9. 3. Bias is present in each of the following sample designs
3. Bias is present in each of the following sample designs. In each case, identify the type of bias involved and state whether you think the sample proportion obtained is higher or lower than the true population proportion. a) A political pollster is seeking information on public attitudes toward funding of pornographic art by the National Endowment for the Arts (NEA). He asks an SRS of 2000 U.S. adults, “Rather than support government censorship of artistic expression, are you in favor of continuing federal funding of artists whose work may be controversial?” 85% of those surveyed answer “yes.” Wording of question bias: it’s possible that using the phrase “government censorship of artistic expression” generates a positive response more often than a more neutral phrase, so that 85% is an overestimate of support.

10. b) In 2003, the AARP conducted a survey of their members (people over age 50 who pay membership dues) on proposed Medicare legislation. One of the questions was: “Even if this plan won’t affect you personally either way, do you think it should be passed so that people with low incomes or people with high drug costs can be helped?” 75% of respondents answered yes. Because the survey is only given to people over 50 who have paid to join AARP, the survey suffers from undercoverage of the young and those who do not have enough income to pay for membership in AARP. Thus the survey will probably underestimate support for the program. (There are other plausible answers, such as wording of the question or response bias).