Chapter 6.5, Problem 55E

The paper “Predictors of Complementary Therapy Use Among Asthma Patients: Results of a Primary Care Survey” (Health and Social Care in the Community [2008]: 155–164) included the accompanying table. The table summarizes the responses given by 1077 asthma patients to two questions:

Question 1: Do conventional asthma medications usually help your asthma symptoms?

Question 2: Do you use complementary therapies (such as herbs, acupuncture, aroma therapy) in the treatment of your asthma?

Consider a chance experiment that consists of randomly selecting one of the 1077 survey participants.

1. a. Construct a joint probability table by dividing the count in each cell of the table by the sample size n = 1077. (Hint: See Example 6.16.)
2. b. The joint probability in the upper left cell of the table from Part (a) is $\frac{816}{1077}=0.758$. This represents the probability of conventional medications usually help and does not use complementary therapies. Interpret the other three probabilities in the joint probability table of Part (a).
3. c. Are the events

CH = event that the selected participant reports that conventional medications usually help

  and

CT = event that the selected participant reports using complementary therapies

  independent events?

Use a probability argument to justify your choice. (Hint: See Example 6.18.)