A drug company wants to investigate whether people feel more energised if they take vitamin supplements. Each week each person categorises their energy level as one of High, Medium and Low, and they also record whether they took the supplements that week. The results for one person are as follows: Performance High Medium Low Yes 14 Supplements? No 7 4 5 (a) Calculate the row and column totals. (b) Calculate the joint and marginal probability distributions. (c) Calculate the conditional probability distribution for the person's performance for the weeks when they took the supplements.
A drug company wants to investigate whether people feel more energised if they take vitamin supplements. Each week each person categorises their energy level as one of High, Medium and Low, and they also record whether they took the supplements that week. The results for one person are as follows: Performance High Medium Low Yes 14 Supplements? No 7 4 5 (a) Calculate the row and column totals. (b) Calculate the joint and marginal probability distributions. (c) Calculate the conditional probability distribution for the person's performance for the weeks when they took the supplements.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Transcribed Image Text:A drug company wants to investigate whether people feel more energised
if they take vitamin supplements. Each week each person
categorises their energy level as one of High, Medium and Low,
and they also record whether they took the supplements that week.
The results for one person are as follows:
Performance
High Medium Low
14
Yes
6
Supplements?
7 4
No
5
(a) Calculate the row and column totals.
(b) Calculate the joint and marginal probability distributions.
(c) Calculate the conditional probability distribution for the person's
performance for the weeks when they took the supplements.
(d) If we're told that the person's energy level in a given week was
High, what is the probability that they took the supplements that
week?
(e) (i) Explain what is meant by two discrete variables being independent,
in terms of their probability distributions.
(ii) Show that the person's energy level is not independent of whether
they took the supplements.
(iii) The drug company claims that
Given the result in part (ii), our experiment proves that taking
vitamin supplements affects a person's energy level.
Is this an accurate claim?
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