The Carolina Reaper Pepper Is Considered One of the Hottest

question 23

Multiple Choice

The Carolina Reaper pepper is considered one of the hottest peppers in the world. However, manufacturers of sauces made from Carolina Reaper often overstate the pungency given on the package to separate their product and ensure sales. An independent laboratory provided a multiple regression model for determining the pungency of the sauce based on a sample of n = 20 sauces. ​ y = Pungency of a sauce (Scoville heat units) ​ x₁ = Carolina Reaper content (%) ​ x₂ = Sugar content (%) ​ x₃ = Vinegar content (%) ​ The estimated regression function was and R² = 0.979. Does the result of a model utility test at α = 0.01 indicate that this multiple regression model is useful? Assume that the random deviation distribution is normal. ​

• A) P-value < 0.001, there appears to be a useful linear relationship between y and each of the three predictors.
• B) P-value > 0.01, there is no useful linear relationship between y and any of the predictors.
• C) P-value < 0.001, there appears to be a useful linear relationship between y and at least one of the three predictors.
• D) 0.001< P-value < 0.01, there is a useful linear relationship between y and each of the three predictors.
• E) P-value > 0.01, there is no useful linear relationship between y and at least one of the predictors.

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Definitions:

Anxious and Inhibited Temperament

A temperament characterized by a predisposition towards anxiety, fearfulness, and shyness, particularly in unfamiliar situations.

Heart Rates

The quantity of heart pulses within a given time frame, usually measured in beats per minute (BPM).

High and Invariable

Describes something that consistently occurs at a great intensity, level, or degree without variation.

Low and Variable

Describes something that not only possesses minimal intensity or quantity but also fluctuates or changes often.