A manufacturer makes ball bearings that have a target diameter of 5\text{ mm}5 mm5, start text, space, m, m, end text. Quality control engineers sample ball bearings from a batch to test the hypotheses H_0: \mu = 5\text{ mm}H 0 :μ=5 mmH, start subscript, 0, end subscript, colon, mu, equals, 5, start text, space, m, m, end text vs. H_\text{a}: \mu \neq 5\text{ mm}H a :μ =5 mmH, start subscript, start text, a, end text, end subscript, colon, mu, does not equal, 5, start text, space, m, m, end text, where \muμmu is the true mean diameter of the ball bearings in that batch. Suppose that H_0H 0 H, start subscript, 0, end subscript is actually true. Which situation below would have the lowest probability of a Type I error?

answer: translate the circles so they share a common center point and dilate circle y by a scale factor of 3.

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!

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