1.A researcher was interested in the effects of eating fruit on learning in elementary school children. She went to the cafeteria of an elementary school and identified 27 students who were eating fruit and 25 who were not. The researcher then compared the grades of those eating fruit with the grades of those who did not eat fruit. a. Is this an observational study or a controlled experiment? Explain.
b. Suppose she found the test scores for those that ate fruit were higher than for those that did not eatfruit. Assume that this was a well-designed study. Can you conclude that eating fruit causes higher test scores? Why or Why not?
c. Identify the population and sample.The population isThe sample is
MATD 0485: Developing Mathematical ThinkingExam: Unit 2A 2 of 62.A group of 600 patients who suffer from migraine headaches are asked to participate in a study to determine the effectiveness of a new medication to reduce the number of headaches. The researchers divided the patients randomly into two groups, one was given the actual medication and one receiveda placebo pill. The researchers recorded the number of headaches each person experienced. Over 6 months of treatment 71% of the patients who took the medication reported fewer headaches, while only 37% of those who took the placebo reported fewer headaches. a.Is this an observational study or a controlled experiment? Explain.b.Assume that this is a well-designed study. Can the researchers conclude that the new medicine causesa decrease in the number of headaches? Why or Why not?c.Identify the four steps of this statistical investigation of headache treatmen