Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the sample has been randomly selected. Select the appropriate response. A manufacturer uses a new production method to produce steel rods. A random sample of 17 steel rods resulted in lengths with a standard deviation of 4.5 cm. Use a 0.10 significance level to test the claim that the new production method has a length standard deviation that is different from 3.5 cm, which was the standard deviation for the lengths using the old method.
Select the correct test statistic and critical value.

A. Test statistic: χ2 = 23.487. Critical values: χ2 = 26.296.
B. Test statistic: χ2 = 26.449. Critical values: χ2 = 26.296.
C. Test statistic: χ2 = 23.487. Critical values: χ2 = 5.623, 29.571.
D. Test statistic: χ2 = 26.449. Critical values: χ2 = 7.962, 26.296.

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step-by-step explanation:

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let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1