A diet center claims that it has the most effective weight loss program in the region. Its advertisements say, "Participants in our program lose more than 3 pounds within a month." Six clients of this program are weighed on the first day of the diet and then one month later. Let the difference be defined as Weight on First Day of Diet minus Weight One Month Later. (You may find it useful to reference the appropriate table: z table or t table) Weight on First weight One Month Later Day of Diet 175 Client 1 166 2 214 204 3 181 175 4 207 185 167 157 6. 153 142 B Click here for the Excel Data File Let the difference be defined as Before - After. a. Specify the null and alternative hypotheses that test the diet center's claim. Họ: HD = 3; HA: HD * 3 O Hạ: HD 2 3; HA: HD < 3 He: HD $ 3; HA: HD > 3 b. Assuming that weight loss is normally distributed, calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic
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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