1. A high-school administrator who is concerned about the amount of sleep the students in his district are getting selects a random sample of 14 seniors in his district and asks them how many hours of sleep they get on a typical school night. He then uses school records to determine the most recent grade-point average (GPA) for each student. His data and a computer regression output are given below. (remember to do ALL parts). (a) Do these data provide convincing evidence of a linear relationship between the hours of sleep students typically get and their academic performance, as measured by their GPA? Carry out a significance test at the α = 0.05 level. (b) Can we conclude from these data that students’ GPA will improve if they get more sleep? Explain
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.
1. A high-school administrator who is concerned about the amount of sleep the students in his district are getting selects a random sample of 14 seniors in his district and asks them how many hours of sleep they get on a typical school night. He then uses school records to determine the
most recent grade-point average (GPA) for each student. His data and a computer regression output are given below. (remember to do ALL parts).
(a) Do these data provide convincing evidence of a linear relationship between the hours of sleep students typically get and their academic performance, as measured by their GPA? Carry out a significance test at the α = 0.05 level.
(b) Can we conclude from these data that students’ GPA will improve if they get more sleep? Explain
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 1 images
