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Is honey a cough remedy?Refer to the Archives of Pediatrics and Adolescent Medicine(Dec. 2007) studyof honey as a remedy for coughing, Exercise 2.31 (p. 86). Recall that the 105 ill children in the sample wererandomly divided into three groups: those who receiveda dosage of over-the-counter cough medicine (DM),those who received a dosage of honey (H), and thosewho received no dosage (control group). The coughingimprovement scores (as determined by the children’sparents) for the patients are reproduced in the nexttable.

Honey Dosage	12, 11, 15, 11, 10, 13, 10, 4 ,15, 16, 9, 14, 10, 6, 10, 8, 11, 12, 12, 8, 12, 9, 11, 15, 10, 15, 9, 13, 8, 12, 10, 8, 9, 5, 12
DM Dosage	4, 6, 9, 4, 7, 7, 7, 9, 12 ,10, 11, 6, 3, 4, 9, 12, 7, 6, 8, 12, 12, 4, 12, 13, 7, 10
No Dosage (Control)	13, 9, 4, 4, 10, 15, 9, 5, 8, 6, 1, 0, 8, 12, 8, 7, 7, 1, 6, 7, 7, 12, 7, 9, 7, 9, 5, 11, 9, 5, 6, 8, 8, 6, 7, 10, 9, 4, 8, 7, 3, 1, 4, 3

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.)

Step by step solution

01

Finding the median improvement score for the honey dosage group

Arranging the data in ascending order,

(4, 5, 6, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 14, 15,15, 15, 15, 16)

As there are an odd number of observations (35), the median is the 18^th number i.e., 11.

Therefore, the median is 11.

02

Calculating the median improvement score for the DM dosage group

Organizing the data for DM dosage in ascending order,

(3, 4, 4, 4, 4, 6, 6, 6, 7, 7, 7, 7, 7, 8, 9, 9, 9, 10,10, 11, 12, 12, 12, 12, 12, 13)

As the observations are even, the calculation for the median will be as follows:

$$\begin{gathered} Median=\frac{Sumoftwovaluesinthecenter}{2} \\ =\frac{7+8}{2} \\ =\frac{15}{2} \\ =7.5 \end{gathered}$$

The median is 7.5.

03

Estimating the median improvement score for the control group

Noting the observations from smaller to bigger values,

(0, 1, 1, 1, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 11, 12, 12, 13, 15)

Due to even number of observations, the median will be,

$$\begin{gathered} Median=\frac{Sumoftwovaluesinthecenter}{2} \\ =\frac{7+7}{2} \\ =\frac{14}{2} \\ =7 \end{gathered}$$

The median for the control group is 7.

04

Conclusion for pediatric researchers

Pediatric researchers can conclude that the improvement data for the control group is the lowest, preceded by the DM dosage group. The improvement data for the honey dosage group is the highest. Therefore, pediatrics should use honey as a treatment for cough.

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