Assume That a Hypothesis Test to Reject the Given Claim

question 161

Multiple Choice

Assume that a hypothesis test to reject the given claim will be conducted. Identify the type I or type II error for the test.
-A manufacturer claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation of 3.3 mg. Identify the type II error for the test.

• A) Reject the claim that the standard deviation is 3.3 mg when it is actually equal to 3.3 mg.
• B) Fail to reject the claim that the standard deviation is 3.3 mg when the standard deviation is actually equal to 3.3 mg.
• C) Reject the claim that the standard deviation is 3.3 mg when it is actually different from 3.3 mg.
• D) Fail to reject the claim that the standard deviation is 3.3 mg when the standard deviation is actually different from 3.3 mg.

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Definitions:

Hypothetical Syllogism

A logical argument consisting of two conditional statements and a conclusion, based on the premise that if one condition is true, then a second condition must follow.

Modus Tollens

A form of logical argument where the denial of the consequent leads to the denial of the antecedent, symbolically represented as "If P then Q; not Q; therefore not P."

Hypothetical

Based on or serving as a hypothesis, suggesting a possible scenario or assumption for the sake of argument.

Hypothetical Syllogism

A form of logical argument involving two conditional statements and a conclusion that infers a relationship based on the preceding premises.