An Engineer Was Investigating the Relationship Between the Thrust of an Experimental

question 19

Short Answer

An engineer was investigating the relationship between the thrust of an experimental rocket (y), the percent composition of a secret chemical in the fuel (x₁) and the internal temperature of a chamber of the rocket (x₂). The engineer starts by fitting a quadratic model, but he believes that the full quadratic model is too complex and can be reduced by only including the linear terms and the interaction term.
The engineer obtained a random sample of 66 measurements and computed the SSE for both the complete model and the reduced model. The values were 1477.8 and 1678.8, respectively. Perform the appropriate test of hypothesis to determine whether the reduced model is adequate for the engineer's use. Use = 0.05.
Test statistic:
F = ______________
What is the critical value of F?
______________
Conclude:
______________ .
There ______________ evidence to indicate that at least one of the two quadratic variables is contributing significant information for predicting y.

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Definitions:

Radioactivity

The spontaneous emission of radiation from the nucleus of an unstable atom as it changes to a more stable state.

Poisson Distribution

A probability distribution that measures the probability of a given number of events happening in a fixed interval of time or space.

Unsafe Levels

Conditions or thresholds that exceed the accepted or legal safety limits, posing risks to health or safety.

Radioactivity

The spontaneous emission of radiation from the nucleus of an unstable atom as it changes to a more stable form.