Determine Which, If Any, of the Three Statements Are Equivalent

question 170

Multiple Choice

Determine which, if any, of the three statements are equivalent.
-I. Gasoline costs $1.99 per gallon if and only if you live in Cook County.
II. You do not live in Cook County and gasoline does not cost $1.99 per gallon.
III. If you do not live in Cook County then gasoline does not cost $1.99 per gallon and if gasoline Does not cost $1.99 per gallon then you do not live in Cook County.

• A) I and II are equivalent
• B) I and III are equivalent
• C) II and III are equivalent
• D) None are equivalent

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Definitions:

Significance Level

The probability of rejecting the null hypothesis when it is true, often denoted by alpha (α).

Chance

The occurrence of events in the absence of any deliberate intention or predictable causation, often used to describe random variability in data.

Confidence Interval

A range of values derived from sample data that is likely to contain the true population parameter with a certain level of confidence.

Statistically Significant

Indicates that an observed effect or result is unlikely to have occurred by chance, suggesting a real impact or difference that is not due to random variation.