For the Conjecture, "The Average Weight of a Cuckoo Bird $\mathrm { A } \mathrm { H } _ { 0 }$

question 57

Essay

For the conjecture, "The average weight of a cuckoo bird is less than or equal to 2.5 pounds," the null and alternative hypotheses are: $\mathrm { A } \mathrm { H } _ { 0 }$ : The average weight of a cuckoo bird is less than or equal to $2.5$ pounds - $\mathrm { H } _ { \mathrm { A } }$ : The average weight of a cuckoo bird is less than $2.5$ pounds
$\mathrm { B } ^ { \mathrm { H } } \mathrm { H } _ { 0 }$ : The average weight of a cuckoo bird is equal to $2.5$ pounds
$\mathrm { H } _ { \mathrm { A } }$ : The average weight of a cuckoo bird is less than or equal to $2.5$ pounds C. $\mathrm { H } _ { 0 }$ : The average weight of a cuckoo bird is more than or equal to $2.5$ pounds $\mathrm { H } _ { \mathrm { A } }$ : The average weight of a cuckoo bird is less than $2.5$ pounds
$\mathrm { D } \mathrm { H } _ { 0 }$ : The average weight of a cuckoo bird is less than or equal to $2.5$ pounds . $\mathrm { H } _ { \mathrm { A } }$ : The average weight of a cuckoo bird is more than $2.5$ pounds

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Definitions:

Validity

The property of an argument in which the truth of the premises logically guarantees the truth of the conclusion.

Hypothetical Syllogism (HS)

A logical argument consisting of two conditional statements and a conclusion that is logically inferred from them.

Modus Ponens (MP)

A logical rule stating that if a conditional statement ("if p then q") is accepted, and the antecedent (p) is also accepted, then the consequent (q) must be accepted.

Modus Tollens (MT)

A form of logical argument where the contrapositive is taken: if P implies Q and Q is false, then P must also be false.