1. Researchers compared the effectiveness of a mood induction technique. They believed that more time exposed to a sad movie, the more depressed the participants will become. Researchers predict that cach increase in time exposed, the greater the depression: 10 minutes will be greater than control, and 20 minutes will be greater than 10. There were 3 different groups of 14 participants cach: 0 minutes exposure (Control Group), 10 minutes exposure, & 20 minutes exposure. The response variable is the score on the Beck Depression Inventory (higher score = more depressed mood). Analyze the data using alpha= .05. %3D Control 10 minutes 20 minutes X=8 SSi= 56 X 11 X-13 SS3 = 62 SS3 = 96 n = 14 n=14 ns = 14 SSTel 368 A. State the hypotheses. B. Make a decision about the null. C. State your conclusion. D. Relate your conclusion to the research E. Are you allowed to conduct analytical comparisons? Yes or no? Why? a. If yes, which groups would you compare? If not allowed, state n'a. b. Regardless of whether you are allowed to conduct analytical comparisons or not, conduct a planned comparison between the control group and the 20 minutes group. Use alpha = .05. i State the hypothesis. ii. Make a decision about the null. iii. State conclusion regarding your planned comparison. iv. Relate your conclusion to the research. ...
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.
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