Problem Set 4: age_at_onset_and_severity.csv

A scientist is trying to understand how age of onset impacts the severity of chicken pox (varicella). The collected data are in age_at_onset_and_severity.csv. These data show age of onset of chicken pox and a self-reported measure of severity (on a scale of 1 through 10; 10 being the most severe) for 800 children.

1. Provide an appropriate graph showing the raw data.

2. What is the statistical hypothesis, and which statistical test is most appropriate?

3. Provide a numeric and verbal description of the output of the statistical test. Is all the output interpretable in the context of the question? (if not, specify which and why)

4. What is the predicted severity, with 95% confidence interval, of a child that contracts the virus at age 5? Do you think the prediction is good?

5. Should the scientist use these results to predict symptom severity for an individual in their 20s? Why or why not?

ParticipantAge	SymptomSeverity
8	3
9	1
12	1
10	7
3	10
10	6
7	7
3	6
3	5
4	3
6	10
3	8
7	5
5	3
10	2
10	7
10	2
11	1
7	7
4	5
5	1
4	7
10	4
4	3
4	5
8	1
6	7
3	5
7	2
10	8
8	6
7	6
5	4
12	3
3	10
5	7
7	7
8	4
12	5
8	4
9	4
5	6
6	6
8	7
8	3
6	8
5	8
5	5
10	5
3	10
6	6
5	4
6	4
8	5
11	1
12	5
5	6
8	2
5	5
12	5
12	5
3	9
11	3
12	3
7	7
5	8
8	6
4	6
8	4
7	8
10	1
7	6
5	4
6	1
9	6
7	8
6	2
3	7
8	4
4	1
3	8
12	4
7	9
10	5
12	5
5	10
12	7
7	7
7	3
11	1
7	6
10	3
9	8
12	2
11	8
3	8
6	5
4	6
4	5
7	1
11	1
7	5
9	1
6	10
5	8
4	4
10	1
10	1
9	5
10	3
11	4
3	3
3	8
11	5
3	9
3	5
9	1
8	4
4	10
4	6
12	2
4	7
6	8
3	9
12	6
7	4
8	6
6	2
10	5
9	2
3	6
11	1
9	1
11	2
3	8
11	10
7	3
4	6
8	7
12	4
3	10
6	4
6	6
8	5
9	5
9	1
3	6
8	1
7	5
10	6
12	1
3	9
9	4
12	4
5	2
5	5
4	8
4	5
11	1
5	2
12	4
12	1
4	6
9	6
10	9
4	8
9	4
9	4
12	5
3	7
10	3
6	5
10	5
11	6
6	7
4	6
4	6
9	6
9	1
10	7
10	3
9	9
4	6
5	5
9	3
7	6
12	8
6	5
8	4
9	1
9	1
8	7
10	6
12	3
3	7
9	4
9	4
6	10
4	5
8	4
4	4
11	5
8	2
8	9
8	4
3	5
12	6
9	4
5	4
4	7
10	1
11	4
6	4
7	1
3	7
4	9
12	1
5	9
4	6
5	8
7	4
8	7
11	5
5	2
10	4
10	5
4	10
4	5
8	8
7	1
6	4
7	5
10	1
12	3
10	1
6	8
3	4
3	8
5	6
4	6
9	2
5	8
6	4
3	4
6	2
11	1
11	2
3	6
5	4
10	7
9	7
9	4
12	5
3	8
4	4
6	2
8	1
3	7
3	2
6	4
3	2
3	5
5	5
3	1
12	3
8	5
9	6
3	7
10	2
6	9
3	5
12	10
12	4
11	4
10	4
5	9
11	3
7	3
11	3
3	10
11	5
6	5
5	6
10	8
10	1
7	1
7	6
9	5
3	9
4	5
5	4
7	5
5	10
10	7
6	3
9	3
4	2
6	5
12	2
3	5
7	2
11	2
11	1
6	5
9	5
7	7
6	4
12	4
11	2
11	4
11	5
7	9
5	5
4	5
10	7
9	1
7	3
9	3
5	3
3	5
11	1
12	4
12	6
9	3
5	4
8	5
8	7
5	7
9	8
4	5
7	5
4	7
9	5
11	2
9	3
11	6
12	3
10	5
11	1
5	5
7	5
4	5
8	8
10	1
6	8
7	3
7	5
5	2
7	4
10	2
11	1
6	7
5	4
4	5
5	7
10	6
6	10
7	10
11	6
8	2
8	5
5	6
10	5
4	2
7	5
4	6
7	3
5	6
3	8
8	5
11	4
3	5
10	6
10	5
3	4
8	3
12	3
12	4
9	7
10	6
8	2
5	10
8	7
9	1
11	3
9	8
3	4
12	8
6	4
3	4
7	5
11	8
6	4
6	5
12	1
5	2
6	8
10	1
6	5
12	6
9	5
12	4
9	2
5	5
5	6
3	10
11	3
4	5
10	6
11	6
12	3
11	9
12	3
4	3
6	9
4	8
5	8
10	2
10	4
6	8
12	3
8	5
11	6
3	4
7	2
4	6
11	1
6	7
9	7
12	4
3	6
7	1
5	5
5	9
5	3
8	4
7	7
11	3
9	4
5	3
11	3
12	2
6	6
7	4
3	2
12	1
12	3
12	6
6	1
8	2
7	5
6	7
4	6
6	6
8	7
4	3
8	1
9	6
12	1
12	2
8	6
9	3
5	6
5	6
7	3
3	5
7	1
6	6
9	6
9	5
10	2
8	3
5	4
5	5
11	8
9	6
8	8
4	3
10	1
5	7
7	3
3	9
8	2
6	5
9	2
8	3
9	2
10	4
10	3
10	5
8	4
6	8
11	4
6	6
9	1
7	10
6	7
12	1
9	2
4	7
11	7
10	6
8	6
11	9
5	5
11	1
5	8
10	9
12	5
7	5
6	8
9	4
8	5
8	5
3	6
10	2
9	3
3	6
7	4
5	4
3	3
12	2
10	5
7	4
6	6
6	4
8	4
11	2
5	5
8	8
9	9
10	3
8	4
8	5
7	5
7	4
9	4
7	1
10	5
6	10
9	8
11	4
11	1
4	5
5	4
3	7
8	3
6	8
10	3
3	3
11	3
9	2
12	6
4	3
12	3
5	6
3	8
8	6
5	6
9	5
10	1
11	4
6	4
4	8
9	6
8	6
11	5
9	4
5	1
9	5
11	1
8	3
3	6
7	5
9	1
4	5
9	3
11	5
6	9
9	4
9	6
11	1
11	8
5	6
6	4
12	6
11	1
4	4
4	5
4	9
10	3
8	1
5	6
11	4
7	1
7	1
9	6
3	9
12	2
3	4
4	4
12	2
6	9
12	1
7	1
4	1
10	9
10	5
7	6
12	5
11	2
3	7
4	5
3	8
9	7
10	4
7	4
8	7
7	6
3	10
8	4
3	7
6	6
4	6
6	7
3	5
12	8
6	4
11	5
4	7
4	2
6	7
9	4
3	10
10	5
12	4
5	5
6	6
10	8
9	3
9	5
5	9
11	4
10	1
9	4
11	2
7	7
8	4
6	7
12	1
6	5
8	1
6	8
11	2
3	1
5	3
6	3
9	9
7	3
8	5
8	9
11	1
9	4
6	1
6	6
11	2
6	8
8	4
9	6
4	10
8	6
12	8
12	3
10	6
7	5
9	5
4	3
9	4
10	1
11	7
7	7
4	4
4	3
6	10
11	8
11	2
11	1
6	4
3	5
12	3
3	7
8	2
11	1
3	8
10	6
11	8
5	8
8	3
3	7
7	8
4	1
10	2
3	7
3	4
10	8
6	6
4	6
3	7
4	10
9	1
8	1
10	8
10	5
3	6
5	3
7	1
7	2
12	1
7	5
6	7
11	4
8	6
5	4
10	5
5	6
6	3
12	1
11	6
6	8
8	6
7	1
3	5
11	2
4	3
7	4
6	6
11	1
6	8
4	1
6	5
9	4
3	9
4	3
6	5
11	1
10	1
10	5
10	1
3	3
6	10
10	1
3	3
12	3
9	3
10	3
9	3
8	2
7	4
7	7
5	9
11	4
9	10
4	4
12	7
12	5
3	3
3	8
5	3
3	10
7	8
11	4
10	2
10	4
7	1
3	4
7	5
11	3
5	4
12	6
5	4
12	1
3	8
6	3
7	8
11	6
9	4
8	1
7	8
3	6
4	4
11	9
11	3
12	1
12	2
5	10
12	5
11	9
6	3
6	8
12	10