1. Evidence suggests that anxiety disorder may contribute to irritable bowel syndrome (IBS), a condition characterized by nausea, alternating constipation, and diarrhea, and no identifiable gastrointestinal pathology. Researchers administer an online questionnaire regarding IBS symptoms to 10,000 people who have an established diagnosis of anxiety disorder in the United States, Canada, and Mexico. They administer the same questionnaire to another 10,000 people from the same countries who do not have a diagnosis of anxiety disorder. Their findings are tabulated below.

IBS Symptoms No IBS symptoms

Anxiety disorder 4000 6000

No Anxiety disorder 1000 9000

a) What percentage of individuals surveyed have IBS symptoms?

b) What percentage of individuals surveyed have an anxiety disorder?

c) What percentage of those with anxiety disorder have IBS symptoms?

d) List three additional pieces of information you can obtain from the table and explain what they tell you about this sample group?

2. A data set consisting of two types of illnesses, bacterial and viral, and their respective durations is summarized in the table below.

TYPE OF ILLNESS

DURATION Viral Bacterial Total

Short 23 47 70

Moderate 42 38 80

Long 10 6 16

Total 75 91 166

a) Construct the conditional distribution of the variable DURATION for Viral Illnesses. Your answer should be a distribution, not a single value.

b) Construct the conditional distribution of the variable DURATION for Bacterial Illnesses. Your answer should be a distribution, not a single value.

c) Based on your answers to a) and b) determine if one should believe DURATION and TYPE OF ILLNESS are independent or dependent. Explain why you chose independent or dependent to receive credit.

3. Does role at a university affect one's willingness to be vaccinated? The partial results of a survey are in the table below. What should the number of students be so that Role (faculty/student) and willingness to be vaccinated are independent?

role

Willing to be Vaccinated? Student. Faculty Total

Yes 304 57

No 18

Total