P: The percentage of fish born with genetic deformities in Humbolt Lake increased between 1962 and 1982.
(A): (The number of fish in Humbolt Lake with such deformities remained constant during the same period.)
C: Hence, we can conclude that there were fewer fish in Humbolt Lake in 1982 than in 1962.
C: Thus, we know that the risk of genetic deformities did not grow during the period between 1962 and 1982.
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Re: 3073
A change in percent can come about in two (or three) ways:
- a change to the numerator
- a change to the denominator
(- or a change to both)
If I said that last year my school was 50% girls and this year it’s 60% girls, you would probably think that there were more girls this year. That is possible, but not a given. That’s making the common assumption of thinking that the NUMERATOR changed.
It’s possible that the denominator changed. Check out this example.
LAST YEAR
60 girls, 60 boys = 120 total students
% of girls = 60 / 120 = ½ = 50%
THIS YEAR
60 girls, 40 boys = 100 total students
% of girls = 60 / 100 = 60%
There were 60 girls both years. The reason the percentage of girls went from 50% to 60% is because there were fewer boys this year. Fewer boys means that there is a lower total. A lower total means that the name number of girls suddenly counts for a higher percentage.
So in this question, instead of boys and girls, you have genetically deformed and NOT genetically deformed.
If the # of genetically deformed fish stayed the same while the % of deformed fish increased, then we know there was a change to the denominator.
If there were 100 deformed fish in 1962 and 100 deformed fish in 1982, then the only difference in the calculation is
% of deformed fish in 1962 = 100 / total fish in ‘62
% of deformed fish in 1982 = 100 / total fish in ‘82
The denominator would have had to shrink in ’82. That’s why we can conclude there were fewer total fish in ’82.
The other answer is really contradicted by the facts, if we define “risk” as “the probability of being deformed”.
If, for example, 13% of fish were deformed in ’62 and 18% of fish were deformed in ’82, then the “risk” of being deformed went up.
- a change to the numerator
- a change to the denominator
(- or a change to both)
If I said that last year my school was 50% girls and this year it’s 60% girls, you would probably think that there were more girls this year. That is possible, but not a given. That’s making the common assumption of thinking that the NUMERATOR changed.
It’s possible that the denominator changed. Check out this example.
LAST YEAR
60 girls, 60 boys = 120 total students
% of girls = 60 / 120 = ½ = 50%
THIS YEAR
60 girls, 40 boys = 100 total students
% of girls = 60 / 100 = 60%
There were 60 girls both years. The reason the percentage of girls went from 50% to 60% is because there were fewer boys this year. Fewer boys means that there is a lower total. A lower total means that the name number of girls suddenly counts for a higher percentage.
So in this question, instead of boys and girls, you have genetically deformed and NOT genetically deformed.
If the # of genetically deformed fish stayed the same while the % of deformed fish increased, then we know there was a change to the denominator.
If there were 100 deformed fish in 1962 and 100 deformed fish in 1982, then the only difference in the calculation is
% of deformed fish in 1962 = 100 / total fish in ‘62
% of deformed fish in 1982 = 100 / total fish in ‘82
The denominator would have had to shrink in ’82. That’s why we can conclude there were fewer total fish in ’82.
The other answer is really contradicted by the facts, if we define “risk” as “the probability of being deformed”.
If, for example, 13% of fish were deformed in ’62 and 18% of fish were deformed in ’82, then the “risk” of being deformed went up.
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