The following situation models the logic of a hypothesis test. An electrician uses an instrument to test whether or not an electrical circuit is defective. The instrument sometimes fails to detect that a circuit is good and working. The null hypothesis is that the circuit is good (not defective). The alternative hypothesis is that the circuit is not good (defective). If the electrician rejects the null hypothesis, which of the following statements is true?

a. The circuit is definitely defective and needs to be repaired.
b. The circuit is definitely good and does not need to be repaired.
c. The circuit is most likely defective, but it might be good.
d. The circuit is most likely good, but it might be defective.

c. The circuit is most likely defective, but it might be good

Step-by-step explanation:

A hypothesis test is being conducted, where electrician uses an instrument to test whether or not an electrical circuit is defective.

The instrument sometimes malfunctions, it fails to detect that a circuit is good and working.

Null hypothesis = H₀ = Circuit is good and works (not defective)

Alternative hypothesis = Ha = Circuit is not good and doesn't work (defective)

If the electrician rejects the null hypothesis, then it means that the circuit is most likely to be defective, but it might be good since the instrument sometimes malfunctions and fails to detect that the circuit is good. Therefore, option C is the correct option.

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step-by-step explanation:

x^3-4x^2+3x-2/x^2+1

step-by-step explanation:

factor the numerator and denominator and cancel the common factors