Reasoning exersie set 7
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Apr 3, 2024
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Exercise Set #7 – Induction, Probability and Generalization PHIL1600 – Reasoning Skills (Winter 2023)
1. For each of the following enumerative inductions:
(i) identify the target group, sample, and relevant property [0.5 pts]; (ii) indicate whether the argument is strong or weak; if it’s strong, explain what features make
it strong, and if it’s weak, specify the source of the problem (e.g., the sample is too small and/or not representative, language problems, expertise, etc.) [0.5 pts].
NOTE: Assume that the information provided in the premises of each argument is true.
(a) In his most recent adventure, Wade Davis examined 23 plants from the Mimulus gemmiparus plant species and found that 77% of them had the characteristics of being tall, having deep roots, and having yellow flowers. From this observation, he concluded that 77% of all plants from that species have these characteristics.
The target group is Mimulus gemmiparus The sample size is 23 plants The relevant property is the characteristics of the plants. This is a weak argument because the sample size is small compared to the total number of flowers meaning he could have got flowers with those specific genes and not accounting for the majority of the total population of flowers. Also me personally I do not know who Wade Davis is or what he does so it makes it more difficult for me to understand what is going on and if it
is valid.
(b) Toyota Motor Corporation inspected 100 cars produced by the company and found that 20
of them have an engine defect. So, 20% of all cars produced by the company probably have this defect.
The target group is Toyota.
The sample size is 100 cars.
The relevant property is the engine defect. This is a weak argument because of the small
sample size. Not every 20 out of 100 cars will for sure have defects meaning the total number of Toyotas in the world will for sure change this number. In order for this to be
true they would need to test every car to see whether it truly is 20% or not. 2. For the following opinion poll:
(i) specify the the target group, sample, and relevant property, the pollster’s conclusion, and
whether the poll results offer strong support for the pollster’s conclusion [1 pt]; (ii) if the results offer strong support, specify why, and if the results do not offer strong support, specify the source of the problem (e.g., issues with the sample or with the question(s) being asked) [1 pt].
Opinion Poll: The Mayor’s office in Windsor, Ontario wants to find out how many school children have witnessed theft within the city. Staff from the Mayor’s office visit a number of classrooms and engage students in a group discussion about the topic. When asked, no children raised their hands to indicate that they had witnessed theft. Using this information, the Mayor’s office concluded that theft is not a big problem in the community.
The target group is school children who are under study.
The sample is the student who has witnessed theft.
Relevant Property is theft. They have come to the conclusion that theft is not a big problem within the community.
This does not provide strong support for the conclusion and is weak because of hasty generalisation. This is due to the small sample size rather than the whole community. Another issue is the reliability of answers as some students may change their answer based on others answers and or lie due to trying to protect a friend.
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