Determine Whether the Statement Is True or False

question 109

Essay

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
If gives rise to a (constrained) relative extremum of subject to the constraint , then also gives rise to the unconstrained relative extremum of .

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Definitions:

Population Mean

The average value of a particular characteristic within an entire population.

Confidence Intervals

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

Normal Populations

Refers to groups whose underlying distribution follows a normal (Gaussian) distribution, characterized by a symmetric bell-shaped curve.

Confidence Interval

A set of values, taken from data samples, which is predicted to include the value of an unspecified population attribute.