een grades achieved and instructor. Can the chair infer that the grade achieved was independent of the instructor for each class at a 5% level of significance?
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.
This year, several students complained that students
in one section received much higher marks than
those in the other sections of the same course.
The department chair recorded student grades
across the sections in an effort to determine if
there was a relationship between grades achieved
and instructor. Can the chair infer that the grade
achieved was independent of the instructor for each
class at a 5% level of significance?
| Instructor | ||||||
| PA | ML | OK | ST | total | ||
| Grade Achieved | A | 8 | 14 | 9 | 4 | 35 |
| B | 13 | 8 | 11 | 10 | 42 | |
| C | 10 | 4 | 6 | 12 | 32 | |
| D | 6 | 5 | 5 | 10 | 26 | |
| F | 3 | 3 | 5 | 4 | 15 | |
| Total | 40 | 34 | 36 | 40 | 150 |
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