Square Deal

Examples of Square Deal in the following topics:

• The Square Deal

  • Roosevelt's Square Deal focused on conservation of natural resources, control of corporations, and consumer protection.
  • The Square Deal was President Theodore Roosevelt's domestic program.
  • These three demands often are referred to as the "three Cs" of Roosevelt's Square Deal.
  • Trusts and monopolies became the primary target of Square Deal legislation.
  • Photograph of Senator Hepburn, who  sponsored the Hepburn Act, which regulated railroad fares, one of the goals of Roosevelt's Square Deal.

• Unequal Sample Sizes

  • The difference between weighted and unweighted means is a difference critical for understanding how to deal with the confounding resulting from unequal n.
  • When confounded sums of squares are not apportioned to any source of variation, the sums of squares are called Type III sums of squares.
  • When all confounded sums of squares are apportioned to sources of variation, the sums of squares are called Type I sums of squares.
  • As you can see, with Type I sums of squares, the sum of all sums of squares is the total sum of squares.
  • None of the methods for dealing with unequal sample sizes are valid if the experimental treatment is the source of the unequal sample sizes.

• Variance

  • Variance is the sum of the probabilities that various outcomes will occur multiplied by the squared deviations from the average of the random variable.
  • The variance of a data set measures the average square of these deviations.
  • A clear distinction should be made between dealing with the population or with a sample from it.
  • When dealing with the complete population the (population) variance is a constant, a parameter which helps to describe the population.
  • When dealing with a sample from the population the (sample) variance is actually a random variable, whose value differs from sample to sample.

• Radical Functions

  • For now, deal with roots by turning them back into exponents.
  • If the square root of a number is taken, the result is a number which when squared gives the first number.
  • Roots do not have to be square.
  • However, using a calculator can approximate the square root of a non-square number:$\sqrt {3} = 1.73205080757$
  • Writing the square root of 3 or any other non-square number as $\sqrt {3}$ is the simplest way to represent the exact value.

• Chi-Square Probability Table

  • Areas in the chi-square table always refer to the right tail.

• Chi Square Distribution

  • Define the Chi Square distribution in terms of squared normal deviates
  • The Chi Square distribution is the distribution of the sum of squared standard normal deviates.
  • Therefore, Chi Square with one degree of freedom, written as χ2(1), is simply the distribution of a single normal deviate squared.
  • A Chi Square calculator can be used to find that the probability of a Chi Square (with 2 df) being six or higher is 0.050.
  • The Chi Square distribution is very important because many test statistics are approximately distributed as Chi Square.

• Factoring Perfect Square Trinomials

  • When a trinomial is a perfect square, it can be factored into two equal binomials.
  • Note that if a binomial of the form $a+b$ is squared, the result has the following form: $(a+b)^2=(a+b)(a+b)=a^2+2ab+b^2.$ So both the first and last term are squares, and the middle term has factors of $2, $ $a$, and $b,$ where the latter are the square roots of the first and last term respectively.
  • For example, if the expression $2x+3$ were squared, we would obtain $(2x+3)(2x+3)=4x^2+12x+9.$ Note that the first term $4x^2$ is the square of $2x$ while the last term $9$ is the square of $3$, while the middle term is twice $2x\cdot3$.
  • Suppose you were trying to factor $x^2+8x+16.$ One can see that the first term is the square of $x$ while the last term is the square of $4$.
  • Since the first term is $3x$ squared, the last term is one squared, and the middle term is twice $3x\cdot 1$, this is a perfect square, and we can write:

• Student Learning Outcomes

• What is Central Tendency?

  • On the right are people who play a great deal (tournament players).
  • It is based on the concept of the sum of squared deviations (differences).
  • The first row in the table shows that the squared value of the difference between 2 and 10 is 64; the second row shows that the squared difference between 3 and 10 is 49, and so forth.
  • When we add up all these squared deviations, we get 186.
  • So, the sum of the squared deviations from 5 is smaller than the sum of the squared deviations from 10.

• Completing the Square

  • The method of completing the square allows for the conversion to the form:
  • Once completing the square has been performed, the quadratic is easy to solve; because there is only one place where the variable $x$ is squared, the $(x-h)^2$ term can be isolated on one side of the equation, and then the square root of both sides can be taken.
  • This quadratic is not a perfect square.  
  • The closest perfect square is the square of $5$, which was determined by dividing the $b$ term (in this case $10$) by two and producing the square of the result.
  • Solve for the zeros of a quadratic function by completing the square