Tricky Problems

A randomized block design will be used in an experiment to compare two lotions that protect people from getting

sunburned. Which of the following should guide the formation of the blocks?

• Participants in the same block should receive the same lotion.

• Participants should be randomly assigned to the blocks.

• Participants should be kept blind as to which block they are in.

• Participants within each block should be as similar as possible with respect to how easily they get sunburned.

The director of a fitness center wants to examine the effects of two exercise classes (spinning and aerobics) on body fat percentage. A six-week spinning class and a six-week aerobics class are offered at the same time and on the same days, so that a person can enroll in only one of them. A new class of each is about to begin, and each class has 25 people in it. Ten people are randomly selected from each class. Each person's body fat percentage is measured at the beginning and again at the end of the six-week class. Using the change in body fat percentage as the response variable and conducting a test at the a = 0.01 level, the director determines that there is a significant difference between the treatment means. Which of the following is a confounding variable in the study?

• The director's choice of spinning and aerobics classes as the types for use in the study.

• The random sample of 10 people from each class.

• The participants' choice of which class to take.

• The use of body fat percentage as the measure of effectiveness of the treatment.

A large simple random sample of people aged nineteen to thirty living in the state of Colorado was surveyed to determine which of two MP3 players just developed by a new company was preferred. To which of the following populations can the results of this survey be safely generalized?

• Only people aged nineteen to thirty living in the state of Colorado who were in this survey

• Only people aged nineteen to thirty living in the state of Colorado

• All people living in the state of Colorado

• Only people aged nineteen to thirty living in the United States

In a recent poll of 1,500 randomly selected eligible voters, only 525 (35 percent) said that they did not vote in the last election. However, a vote count showed that 80 percent of eligible voters actually did not vote in the last election. Which of the following types of bias is most likely to have occurred in the poll?

• Nonresponse bias

• Selection bias

• Undercoverage bias

• Response bias

A recent study examined 699 car accidents in Toronto over a fourteen-month period. Records of phone-service

providers were used to determine whether the driver was using a cell phone during or immediately before the

accident. Overall, the researchers found that drivers using cell phones were 4.3 times as likely to have an accident as

drivers who were not using cell

• Cell phone use increases the likelihood of a car accident.

• There is an association between cell phone use and accidents, but not necessarily a causal relationship.

• There is a correlation between cell phone use and accidents, but not necessarily an association.

• The association between cell phone use and accidents is negative.

survey was administered to parents of high school students in a certain state to see if the parents thought the

students’ academic needs were being met. To select the sample, the parents were divided into two groups— one

group of parents who live in cities with populations of more than 100,000 and the other group of parents who live in

cities with populations less than or equal to 100,000. A random sample of 100 parents from each group was taken.

Which of the following statements about the sample of 200 parents is true?

• It is a convenience sample because the sample of parents was easily obtained.

• It is a stratified random sample because parents were randomly selected from each group.

• It is a random cluster sample because parents were randomly selected from each group.

• It is a systematic sample because the parents were systematically divided into two groups.

A regional transportation authority is interested in estimating the mean number of minutes working adults in the

region spend commuting to work on a typical day. A random sample of working adults will be selected from each of

three strata: urban, suburban, and rural. Selected individuals will be asked the number of minutes they spend

commuting to work on a typical day. Why is stratification used in this situation?

• To remove bias when estimating the proportion of working adults living in urban, suburban, and rural areas

• To reduce bias when estimating the mean commuting time

• To decrease the variability in estimates of the proportion of working adults living in urban, suburban, and

  rural areas

• To decrease the variability in estimates of the mean commuting time

Can texting make you healthier? Researchers randomly assigned 700 Australian adults to either receive usual health care or usual health care plus automated text messages with positive messages, such as "Walking is cheap. It can be done almost anywhere. All you need is comfortable shoes and clothing." The group that received the text messages showed a statistically significant increase in physical activity. What is the meaning of "statistically significant" in this context?

• The results of this study are very important

• The results of this study should be generalized to all people

• The difference in physical activity for the two groups is greater than 0

• The difference in physical activity for the two groups is very large

• The difference in physical activity for the two groups is larger than the difference that could be expected to happen by chance alone

The most important advantage of experiments over observational studies is that

• experiments are usually easier to carry out

• experiments can give better evidence of causation

• confounding cannot happen in experiments

• an observational study cannot have a response variable

• observational studies cannot use random samples

A gardener want to try different combinations of fertilizer (none, 1 cup, 2 cups) and mulch (none, wood chips, pine needles, plastic) to determine which combination produces the highest yield for a variety of green beans. He has 60 green-bean plants to use in the experiment. If he wants an equal number of plants to be assigned to each treatment, how many plants will be assigned to each treatment?

• 1

• 3

• 4

• 5

• 12