Question

Introduction to Probability and Statistics

Is honey a cough remedy?

Does a teaspoon of honey before bed really calm a child’s cough? To test the folk remedy, pediatric researchers carried out a designed study involving a sample of 105 children who were ill with an upper respiratory tract infection.

On the first night, parents rated their children’s cough symptoms on a scale from 0 (no problems at all) to 30 (extremely severe). On the second night, the parents were instructed to give their sick child a dosage of liquid “medicine” prior to bedtime.

Unknown to the parents,
• a first group: are given a dose of honey.
• a second group: are given a similar dosage of dextromethorphan (DM), i.e., cough medicine.
• a third group (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 is given below:

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 13 9 4 4 10 15 9

No Dosage (Control): 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

Question. Use R to construct a side-by-side boxplot for the three groups of data. From this plot:
(a) Can you conclude that a teaspoon of honey before bed really calms a child’s cough? Explain
(b) State which group appears to have the most variability in coughing improvement scores? The least variability? Explain
(c) Identity, if any, the outliers in each group.

Answer 1

We have used R software to plot the data

the plot is

(a) Can you conclude that a teaspoon of honey before bed really calms a child’s cough? Explain

here we have seen that the rating for honey as cough medicine got highest among 3 methods. Hence we can comment that the honey as cough remedy works best among 3 as per rating.

(b) State which group appears to have the most variability in coughing improvement scores? The least variability? Explain

Variability can be noted from the graph that has highest spread. We can note that the DM method has highest spread as medicine.

(c) Identity, if any, the outliers in each group.

outliers of each group mentioned as a dot in graph

for control : rating 1 is a outlier

for DM: no outlier

for honey : rating 4 is a outlier.

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