You Have Supplies of Boards That Are One Foot, fiVe

question 42

Essay

You have supplies of boards that are one foot, five feet, seven feet, and twelve feet long. You need to lay pieces end-to-end to make a molding 15 feet long and wish to do this using the fewest number of pieces possible. Explain why the greedy algorithm of taking boards of the longest length at each stage (so long as the total length of the boards selected does not exceed 15 feet) does not give the fewest number of boards possible.

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Definitions:

Level Of Significance

The level of significance, often denoted by alpha, is a threshold set for deciding whether to reject the null hypothesis, typically set at values like 0.05 or 0.01.

Rejection Region

The rejection region is the range of values in hypothesis testing that leads to the rejection of the null hypothesis if the test statistic falls within this range.

Robust Estimator

An estimate method that is not overly sensitive to outliers or violations of assumptions by the underlying data-generating process.

Normality

In statistics, a condition in which a distribution approximates the normal distribution, characterized by a bell-shaped curve.