Vitamin C for marathon runners An ultramarathon, as you might guess, is a footrace longer than the

$26.2$ miles of a marathon. Runners commonly develop respiratory infections after an ultramarathon. Will taking $600$ milligrams of vitamin C daily reduce those infections? Researchers randomly assigned ultramarathon runners to receive either vitamin C or a placebo. Separately, they also randomly assigned these treatments to a group of nonrunners the same age as the runners. All subjects were watched for $14$ days after the big race to see if infections developed.

(a) What type of experimental design did the researchers use? Why is this design preferable in this setting? Give one reason.

(b) Explain the purpose of the random assignment.

(c) The report of the study said: “Sixty-eight percent of the runners in the placebo group reported the development of symptoms of upper respiratory tract infection after the race; this was significantly

A footrace longer than the $26.2$ miles of a long-distance race is known as an ultra-long-distance race.

The random assignment method assigns subjects to treatments based on chance. Before the treatments are applied, random assignment establishes treatment groups that are comparable (except for chance variance). In experiments, randomization and comparison combined prevent bias or systematic favoritism.

A footrace longer than the $26.2$ miles of a long-distance race is known as an ultra-long-distance race. After ultra-long-distance races, sprinters frequently get respiratory problems, thus scientists randomly assigned ultra-long-distance runners to receive either nutritional C or a placebo treatment. Stratified random samples are samples taken from different strata in a diverse population using simple random sampling. Because a sample from each group might be selected and then all of the selected groups would be equally represented in the chosen sample, the stratified random sample sampling method should be utilized.

Random assignment is mostly used to form groups and reduce bias in the final outcome. As a result, it would be used to eliminate prejudice and influence the outcome.

The placebo rate of $68$ percent is much greater than the vitamin rate of $33$ percent, implying that the observed difference is excessive.