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DRAWING CONCLUSIONS A company wants to test whether a nutritional supplement has an adverse effect on an athlete’s heart rate while exercising. Identify a potential problem, if any, with each experimental design. Then describe how you can improve it. (See Example 3.) a. The company randomly selects 250 athletes. Half of the athletes receive the supplement and their heart rates are monitored while they run on a treadmill. The other half of the athletes are given a placebo and their heart rates are monitored while they lift weights. The heart rates of the athletes who took the supplement signifi cantly increased while exercising. b. The company selects 1000 athletes. The athletes are divided into two groups based on age. Within each age group, the athletes are randomly assigned to receive the supplement or the placebo. The athletes’ heart rates are monitored while they run on a treadmill. There was no signifi cant difference in the increases in heart rates between the two groups.

In Exercises 9–12, identify the type of sample and explain why the sample is biased. You want to find out whether booth holders at a convention were pleased with their booth locations. You divide the convention center into six sections and survey every booth holder in the fifth section.

2\. DRAWING CONCLUSIONS A researcher wants to test the effectiveness of reading novels on raising intelligence quotient (IQ) scores. Identify a potential problem, if any, with each experimental design. Then describe how you can improve it. a. The researcher selects 500 adults and randomly divides them into two groups. One group reads novels daily and one group does not read novels. At the end of 1 year, each adult is evaluated and it is determined that neither group had an increase in IQ scores. b. Fifty adults volunteer to spend time reading novels every day for 1 year. Fifty other adults volunteer to refrain from reading novels for 1 year. Each adult is evaluated and it is determined that the adults who read novels raised their IQ scores by 3 points more than the other group

Surveys are mailed to every other household in a neighborhood. Each survey that is returned is used. Describe and correct the error in identifying the type of sample that is used. Because the surveys were mailed to every other household, the sample is a systematic sample.

WRITING Explain why observational studies, rather than experiments, are usually used in astronomy

Describe an example of an observation that can be made from an experiment. Then give four possible inferences that could be made from the observation.

Factor the polynomial completely. \(y^3-8\)

In Exercises 15–18, determine whether the sample is biased. Explain your reasoning. To assess customers' experiences making purchases online, a rating company e-mails purchasers and asks that they click on a link and complete a survey.

ERROR ANALYSIS A survey of 1270 high school students found that 965 students felt added stress because of their workload. Describe and correct the error in identifying the population and the sample.

WRITING Describe the placebo effect and how it affects the results of an experiment. Explain how a researcher can minimize the placebo effect.