A new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of 62 women over the age of 50 used the new cream for 6 months. Of those 62 women, 36 of them reported skin improvement(as judged by a dermatologist). Is this evidence that the cream will improve the skin of more than 50% of women over the age of 507 Test using a = 0.01. (a) Test statistic: z- (b) Critical Value: z (c) The final conclusion is A. There is not sufficient evidence to reject the null hypothesis that p= 0.5. That is, there is not sufficient evidence to reject that the cream can improve the skin of more than 50% of women over 50. OB. We can reject the null hypothesis that p = 0.5 and accept that p> 0.5. That is, the cream can improve the skin of more than 50% of women over 50. ltemnt ir ?3%
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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