The familial aggregation of respiratory disease is a well-established clinical phenomenon. However, whether this aggregation is due to genetic or environmental factors or both is somewhat controversial. An investigator wishes to study a particular environmental factor, namely the relationship of cigarette-smoking habits in the parents to the presence or absence of asthma in their oldest child age 5 to 9 years living in the household (referred to below as their offspring). Suppose the investigator finds that (1) if both the mother and father are current smokers, then the probability of their offspring having asthma is .15; (2) if the mother is a current smoker and the father is not, then the probability of their offspring having asthma is .13; (3) if the father is a current smoker and the mother is not, then the probability of their offspring having asthma is .05; and (4) if neither parent is a current smoker, then the probability of their offspring having asthma is .04. Suppose, alternatively, that if the father is a current smoker, then the probability that the mother is a current smoker is .6; whereas if the father is not a current smoker, then the probability that the mother is a current smoker is .2. Also assume that statements 1, 2, 3, and 4 above hold. Answer Problem 3.59 if the child does not have asthma. 3.59 What is the posterior probability that the mother is a current smoker if the child has asthma?
The familial aggregation of respiratory disease is a well-established clinical phenomenon. However, whether this aggregation is due to genetic or environmental factors or both is somewhat controversial. An investigator wishes to study a particular environmental factor, namely the relationship of cigarette-smoking habits in the parents to the presence or absence of asthma in their oldest child age 5 to 9 years living in the household (referred to below as their offspring). Suppose the investigator finds that (1) if both the mother and father are current smokers, then the probability of their offspring having asthma is .15; (2) if the mother is a current smoker and the father is not, then the probability of their offspring having asthma is .13; (3) if the father is a current smoker and the mother is not, then the probability of their offspring having asthma is .05; and (4) if neither parent is a current smoker, then the probability of their offspring having asthma is .04. Suppose, alternatively, that if the father is a current smoker, then the probability that the mother is a current smoker is .6; whereas if the father is not a current smoker, then the probability that the mother is a current smoker is .2. Also assume that statements 1, 2, 3, and 4 above hold. Answer Problem 3.59 if the child does not have asthma. 3.59 What is the posterior probability that the mother is a current smoker if the child has asthma?
Solution Summary: The author explains the posterior probability that the mother is a current smoker if the child does not have asthma.
The familial aggregation of respiratory disease is a well-established clinical phenomenon. However, whether this aggregation is due to genetic or environmental factors or both is somewhat controversial. An investigator wishes to study a particular environmental factor, namely the relationship of cigarette-smoking habits in the parents to the presence or absence of asthma in their oldest child age 5 to 9 years living in the household (referred to below as their offspring). Suppose the investigator finds that (1) if both the mother and father are current smokers, then the probability of their offspring having asthma is .15; (2) if the mother is a current smoker and the father is not, then the probability of their offspring having asthma is .13; (3) if the father is a current smoker and the mother is not, then the probability of their offspring having asthma is .05; and (4) if neither parent is a current smoker, then the probability of their offspring having asthma is .04.
Suppose, alternatively, that if the father is a current smoker, then the probability that the mother is a current smoker is .6; whereas if the father is not a current smoker, then the probability that the mother is a current smoker is .2. Also assume that statements 1, 2, 3, and 4 above hold.
Answer Problem 3.59 if the child does not have asthma.
3.59 What is the posterior probability that the mother is a current smoker if the child has asthma?
For 25 years, Arthur Reynolds and Judy Temple tracked more than 1,400 children who participated in a publicly funded early childhood development program beginning at age 3. They found that children who participated in the program showed higher levels of educational attainment, socioeconomic status, and job skills, as well as lower rates of substance abuse, felony arrest, and incarceration, than those who did not receive school-based early education. One possible theory for the success of this program is that improving school readiness improved the children's success in school. The improved success in school in turn improved their readiness for adulthood, resulting in increased job skills and socioeconomic status as well as lower rates of substance abuse.
What is the independent and dependent variable?
Question 1)
Consider the following context:
The nutrition and food science division of Farnsworth Pharmaceuticals is alpha testing an OTC diagnostic kit so that adults who self-report a certain food allergy can affirm their insensitivity to that food allergen. Preliminary clinical trials yielded that 25% of the volunteers who suspected they had food allergies were clinically identified as sensitive or intolerant to the food allergen; unfortunately and disappointingly, only 10% of those who tested positive in the clinic also tested positive with the kit. Furthermore, of those self-reporting adult volunteers who had a negative clinic outcome, 5% tested positive anyway with the kit.
How many complete branches, from start to finish, would a tree diagram that models this context include? H
Question 2)
The nutrition and food science division of Farnsworth Pharmaceuticals is alpha testing an OTC diagnostic kit so that adults who self-report a certain food allergy can affirm their…
In the book Business Research Methods (5th ed.), Donald R. Cooper and C. William Emory discuss studying the relationship between on-the-job accidents and smoking. Cooper and Emory describe the study as follows:
Suppose a manager implementing a smoke-free workplace policy is interested in whether smoking affects worker accidents. Since the company has complete reports of on-the-job accidents, she draws a sample of names of workers who were involved in accidents during the last year. A similar sample from among workers who had no reported accidents in the last year is drawn. She interviews members of both groups to determine if they are smokers or not.
The sample results are given in the following table.
On-the-Job Accident
Smoker
Yes
No
Row Total
Heavy
12
5
17
Moderate
9
10
19
Nonsmoker
13
17
30
Column total
34
32
66
Expected counts are below observed counts
Accident
No Accident
Total
Heavy
12
5
17
8.76
8.24…
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