2.12We don't like one-way streets.

Highway planners decided to make a main street in West Lafayette, Indiana, a one-way street. TheLafayette Journal and Couriertook a one-day poll by inviting readers to call a telephone number to record their comments. The next day, the paper reported:

Journal and Courierreaders overwhelmingly prefer two-way traffic flow in West Lafayette's Village area to one-way streets. By nearly a 7-1 margin, callers on Wednesday complained about the one-way streets that have been in place since May. Of the 98 comments received, all but 14 said no to one-way.

1. What population do you think the newspaper wants information about?
2. Is the proportion of this population who favor one-way streets almost certainly larger or smaller than the proportion of 14/98 in the sample? Why?

6.14 Beating sunburn with broccoli.

Some recent studies suggest that compounds in broccoli may be helpful in combating the effects of overexposure to ultraviolet radiation. Based on these studies we hope to show that a cream consisting of a broccoli extract reduces sunburn pain. To do this, we recruit 60 patients suffering from severe sunburn and needing pain relief. We will apply the cream to the sunburn of each patient and ask them an hour later, "About what percent of pain relief did you experience?"

1. Why should we not simply apply the cream to all 60 patients and record the responses?
2. Outline the design of an experiment to compare the cream's effectiveness with that of an over-the-counter product for sunburn relief and that of a placebo.
3. Should patients be told which remedy they are receiving? How might this knowledge affect their reactions?
4. If patients are not told which treatment they are receiving, but the researchers assessing the effect of the treatment know, the experiment is single-blind. Should this experiment be double-blind? Explain

12.16 The richest 5%.

The distribution of individual incomes in the United States is strongly skewed to the right. In 2016, if we only look at the incomes of the top 5% of Americans, the mean and median incomes of the individuals in the top 5% were $215,000 and $375,000. Which of these numbers is the mean and which is the median? Explain your reasoning.

17.24 An eerie coincidence?

A September 13, 2011,New York Postarticle reported that the first three winners at Belmont Park were horses wearing the numbers 9, 1, 1 on the tenth-year anniversary of the 9/11 attacks on America. Should this fact surprise you? Explain your answer.

23.22 Is this convincing?

You are planning to test a vaccine for a virus that now has no vaccine.Because the disease is usually not serious, you will expose 100 volunteers to the virus. After some time, you will record whether or not each volunteer has been infected.

1. Explain how you would use these 100 volunteers in a designed experiment to test the vaccine. Include all important details of designing the experiment (but don't actually do any random allocation).
2. You hope to show that the vaccine is more effective than a placebo. StateH0andHa. (Notice that this test comparestwopopulation proportions.)
3. The experiment gave aP-value of 0.15. Explain carefully what this means.
4. Your fellow researchers do not consider this evidence strong enough to recommend regular use of the vaccine. Do you agree?