paper included the accompanying table. The table summarizes the responses given by 1,079 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? Doesn't Use Complementary Therapies Does Use Complementary Therapies Conventional Medications Usually Help 817 132 Conventional Medications Usually Do Not Help 104 26 Consider a chance experiment that consists of randomly selecting one of the 1,079 survey participants. (a) Construct a joint probability table by dividing the count in each cell of the table by the sample size n = 1,079. (Round your answers to three decimal places.) Doesn't Use Complementary Therapies Does Use Complementary Therapies Conventional Medications Usually Help Conventional Medications Usually Do Not Help (b) The joint probability in the upper left cell of the table from part (a) is 817 1,079 = 0.757. This represents the probability of conventional medications usually help and does not use complementary therapies. Interpret the probability in the upper right cell of the joint probability table of part (a). This cell represents the probability of conventional medicines usually help. This cell represents the probability of conventional medicines usually help and does use complementary therapies. This cell represents the probability of conventional medicines usually does not help and does not use complementary therapies. This cell represents the probability of conventional medicines usually does not help and does use complementary therapies. This cell represents the probability use of complementary therapies. Interpret the probability in the lower left cell of the joint probability table of part (a). This cell represents the probability of conventional medicines usually help. This cell represents the probability of conventional medicines usually help and does use complementary therapies. This cell represents the probability of conventional medicines usually does not help and does not use complementary therapies. This cell represents the probability of conventional medicines usually does not help and does use complementary therapies. This cell represents the probability use of complementary therapies. Interpret the probability in the lower right cell of the joint probability table of part (a). This cell represents the probability of conventional medicines usually help. This cell represents the probability of conventional medicines usually help and does use complementary therapies. This cell represents the probability of conventional medicines usually does not help and does not use complementary therapies. This cell represents the probability of conventional medicines usually does not help and does use complementary therapies. This cell represents the probability use of complementary therapies. (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. No, they are not independent events because P(CH) · P(CT) = P(CH ∩ CT). Yes, they are independent events because P(CH) · P(CT) ≠ P(CH ∩ CT). No, they are not independent events because P(CH) · P(CT) ≠ P(CH ∩ CT). Yes, they are independent events because P(CH) · P(CT) = P(CH ∩ CT).
paper included the accompanying table. The table summarizes the responses given by 1,079 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?
Doesn't Use
Complementary
Therapies
Does Use
Complementary
Therapies
Conventional
Medications Usually
Help
817
132
Conventional
Medications Usually
Do Not Help
104
26
Consider a chance experiment that consists of randomly selecting one of the 1,079 survey participants.
(a)
Construct a joint
Doesn't Use
Complementary
Therapies
Does Use
Complementary
Therapies
Conventional
Medications Usually
Help
Conventional
Medications Usually
Do Not Help
(b)
The joint probability in the upper left cell of the table from part (a) is
817
1,079
= 0.757.
This represents the probability of conventional medications usually help and does not use complementary therapies. Interpret the probability in the upper right cell of the joint probability table of part (a).
This cell represents the probability of conventional medicines usually help.
This cell represents the probability of conventional medicines usually help and does use complementary therapies.
This cell represents the probability of conventional medicines usually does not help and does not use complementary therapies.
This cell represents the probability of conventional medicines usually does not help and does use complementary therapies.
This cell represents the probability use of complementary therapies.
Interpret the probability in the lower left cell of the joint probability table of part (a).
This cell represents the probability of conventional medicines usually help.
This cell represents the probability of conventional medicines usually help and does use complementary therapies.
This cell represents the probability of conventional medicines usually does not help and does not use complementary therapies.
This cell represents the probability of conventional medicines usually does not help and does use complementary therapies.
This cell represents the probability use of complementary therapies.
Interpret the probability in the lower right cell of the joint probability table of part (a).
This cell represents the probability of conventional medicines usually help.
This cell represents the probability of conventional medicines usually help and does use complementary therapies.
This cell represents the probability of conventional medicines usually does not help and does not use complementary therapies.
This cell represents the probability of conventional medicines usually does not help and does use complementary therapies.
This cell represents the probability use of complementary therapies.
(c)
Are the events
CH =
and
CT = event that the selected participant reports using complementary therapies
independent events? Use a probability argument to justify your choice.
No, they are not independent events because P(CH) · P(CT) = P(CH ∩ CT).
Yes, they are independent events because P(CH) · P(CT) ≠ P(CH ∩ CT).
No, they are not independent events because P(CH) · P(CT) ≠ P(CH ∩ CT).
Yes, they are independent events because P(CH) · P(CT) = P(CH ∩ CT).
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