What is a range of values between which the value of the population parameter is believed to be, along with a probability that the interval correctly estimates the true population parameter?

Confidence intervals

Step-by-step explanation:

Confidence intervals offer a way to estimate, with high probability, a range of values in which the population value (or parameter) of a given variable is found.

In simple terms, a 95% confidence interval indicates that the population value is in a certain range of values with 95% certainty. As a general rule, the larger the sample size, the smaller the variability for estimating the interval, leading to more accurate estimators.

this is a very good question

step-by-step explanation:

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1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.