A product development scientist is tasked with determining which of three methods is the most effective for catching fruit flies: a sticky paper trap, a liquid trap, or a container trap. The scientist hypothesizes that all three methods will be equally effective at catching the fruit flies. To investigate, he releases a random sample of 300 fruit flies in an enclosed area containing each of the three traps. What are the appropriate hypotheses?
Answer
A
cap h sub 0 : p sub paper is not equal to 1 third , p sub liquid is not equal to 1 third , p sub container is not equal to 1 third cap h sub A : p sub paper is equal to 1 third , p sub liquid is equal to 1 third , p sub container is equal to 1 third
B
cap h sub 0 : Not all of the p sub i 's are as stated. cap h sub A : p sub paper is equal to 1 third , p sub liquid is equal to 1 third , p sub container is equal to 1 third
C
cap h sub 0 : p sub paper is equal to 1 third , p sub liquid is equal to 1 third , p sub container is equal to 1 third cap h sub A : Not all of the p sub i 's are as stated.
D
cap h sub 0 : p sub paper is equal to 1 third , p sub liquid is equal to 1 third , p sub container is equal to 1 third cap h sub A : p sub paper is not equal to 1 third , p sub liquid is not equal to 1 third , p sub container is not equal to 1 third
Explanation
The scientist’s hypothesis that the three traps are equally effective means each trap should catch one-third of the flies: p_paper = p_liquid = p_container = 1/3. That equality is the null hypothesis. The alternative is that the catches are not equally distributed, meaning at least one proportion differs from 1/3; this matches choice C.
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