Refer to the Archives of Pediatrics and Adolescent Medicine (Dec. 2007) study of honey as a remedy for coughing, Exercise 2.40 (p. 51). Recall that the 105 ill children in the sample were randomly divided into three groups: those who received a dosage of an over-the-counter cough medicine (DM), those who received a dosage of honey (H), and those who received no dosage (control group). The coughing improvement scores for the patients are reproduced in the table below.

Based on Paul, I. M., et al. "Effect of honey, dextromethorphan, and no treatment on nocturnal cough and sleep quality for coughing children and their parents." Archives of Pediatrics and Adolescent Medicine, Vol. 161, No. 12, Dec. 2007 (data simulated)
a. Find the median improvement score for the honey dosage group.
b. Find the median improvement score for the DM dosage group.
c. Find the median improvement score for the control group.
d. Based on the results, parts a-c, what conclusions can pediatric researchers draw? (We show how to support these conclusions with a measure of reliability in subsequent chapters.

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Honey Dosage: 12 11 15 11 10 13 10 4 15 16 8 12 8 12 10 8 11 12 12 6 10 14 10 9 13 11 15 10 15 5 12 4 7 9 12 7 10 13 9 9 12 10 11 8 12 12 DM 4 6 Dosage: 3 4 12 13 4 4 10 15 No Dosage 8 12 5 1. 7 12 (Control): 6 6. 1. 9. 5 11 4 8 7 10 6. 3 9. 4 7. 6784