Pediatric researchers at $ Pennsylvania State University carried out a designed HCOUGH study to test whether a teaspoon of honey before bed calms a child's cough and published their results in Archives of Pediatrics and Adolescent Medicine (Dec. 2007). (This experiment was first described in Exercise 2.30, p. 61.) A sample of 105 children who were ill with an upper respiratory tract infection and their parents participated in the study. On the first night, the parents rated their children's cough symptoms on a scale from 0 (no problems at all) to 6 (extremely severe) in five different areas. The total symptoms score (ranging from 0 to 30 points) was the variable of interest for the 105 patients. On the second night, the parents were instructed to give their sick children a dosage of liquid "medicine" prior to bedtime. Unknown to the parents, some were given a dosage of dextromethorphan (DM) - an over-the-counter cough medicine -while others were given a similar dose of honey. Also, a third group of parents (the control group) gave their sick children no dosage at all. Again, the parents rated their children's cough symptoms, and the improvement in total cough symptoms score was determined for each child. The data (improvement scores) for the study are shown in the accompanying table. The goal of the researchers was to compare the mean improvement scores for the three treatment groups.
a. Identify the type of experimental design employed. What are the treatments?
b. Conduct an analysis of variance on the data and interpret the results.

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Honey 1211 15 11 10 13 10 4 15 16 9 14 Dosage:10 6 10 811 12 12 8 12 9 11 15 10 15 9 13 8 12 10 8 9 5 12 4 6 9 47779 12 10 11 12 13 7 10 13 9 4 4 10 15 9 DM Dosage: 6 3 4 912 7 68 12 12 4 No Dosage 5 86 1 0812 8 7 7 1 6 (Control): 7 7 12 795 119 5 68 8 6 7 109 48731 4 3