In studying the relationship between income and time spent exercising, suppose you computed r=−0.052 using n=19data points. Using the critical values table below, determine if the value of r is significant or not. df CV (+ and -) df CV (+ and -) df CV (+ and -) df CV (+ and -) 1 0.997 11 0.555 21 0.413 40 0.304 2 0.950 12 0.532 22 0.404 50 0.273 3 0.878 13 0.514 23 0.396 60 0.250 4 0.811 14 0.497 24 0.388 70 0.232 5 0.754 15 0.482 25 0.381 80 0.217 6 0.707 16 0.468 26 0.374 90 0.205 7 0.666 17 0.456 27 0.367 100 0.195 8 0.632 18 0.444 28 0.361 9 0.602 19 0.433 29 0.355 10 0.576 20 0.423 30 0.349 Select the correct answer below: a. r is significant because it is between the positive and negative critical values. b. r is not significant because it is between the positive and negative critical values. c. r is significant because it is not between the positive and negative critical values. d. r is not significant because it is not between the positive and negative critical values.
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
| df | CV (+ and -) | df | CV (+ and -) | df | CV (+ and -) | df | CV (+ and -) |
|---|---|---|---|---|---|---|---|
| 1 | 0.997 | 11 | 0.555 | 21 | 0.413 | 40 | 0.304 |
| 2 | 0.950 | 12 | 0.532 | 22 | 0.404 | 50 | 0.273 |
| 3 | 0.878 | 13 | 0.514 | 23 | 0.396 | 60 | 0.250 |
| 4 | 0.811 | 14 | 0.497 | 24 | 0.388 | 70 | 0.232 |
| 5 | 0.754 | 15 | 0.482 | 25 | 0.381 | 80 | 0.217 |
| 6 | 0.707 | 16 | 0.468 | 26 | 0.374 | 90 | 0.205 |
| 7 | 0.666 | 17 | 0.456 | 27 | 0.367 | 100 | 0.195 |
| 8 | 0.632 | 18 | 0.444 | 28 | 0.361 | ||
| 9 | 0.602 | 19 | 0.433 | 29 | 0.355 | ||
| 10 | 0.576 | 20 | 0.423 | 30 | 0.349 |
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