8.2
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This document discusses p-values and hypothesis testing. It reminds the reader to find the p-value, which can be done using Table A or the Normalcdf function in a calculator. The p-value is used to test hypotheses and determine if results are statistically significant.
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2) Federal aid to states, when coordinated, can effectively stimulate the overall economy. Targeted aid linked to services for lower income households is more effective than untargeted aid.
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Since this rather amazing fact was discovered in 1881 by the American astronomer
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We start by establishing a connection between the Microarray and Stock Index
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FISCAL STIMULUS IN ECONOMIC UNIONS: WHAT ROLE FOR STATES
1) State deficits can boost job growth in the deficit state but also in neighboring states, showing significant spillover effects. Coordinated fiscal policies across states are more cost-effective than individual state policies.
2) Federal aid to states, when coordinated, can effectively stimulate the overall economy. Targeted aid linked to services for lower income households is more effective than untargeted aid.
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Newcomb (1881), many scientist have been searching about members of the outlaws
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numbers starting with 1 were much more worn than the other pages. After analyzing
several sets of naturally occurring data Newcomb went on to derive what later became
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7.1
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7.2
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10.1 part2
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10.1 part 1
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5.4 synthetic division
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5.3
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9.1 9.2 9.3 using the graph calc
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5.2
1. The document discusses writing polynomials in factored form and finding the zeros of polynomial functions. It defines linear factors, roots, zeros, and x-intercepts as equivalent terms.
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5.1 part 2
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5.1[1]
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9.1
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9.2 lin reg coeff of det
1) Linear regression finds the "best-fitting" linear relationship between two variables by minimizing the vertical distances between the data points and the linear equation line.
2) The coefficient of determination, r^2, measures how well the linear relationship described by the regression line fits the actual data, with higher r^2 values indicating less unexplained variability.
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7.3 daqy 2
Logarithmic functions are inverses of exponential functions. To graph a logarithmic function:
1. Identify the inverse exponential form.
2. Create a table of values for the exponential form.
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7.2
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This document discusses synthetic division and the remainder theorem. Synthetic division is a process that simplifies long division when dividing a polynomial by a linear factor of the form x - a. It involves setting up the coefficients of the polynomial and multiplying/adding through the process. The remainder theorem states that if a polynomial P(x) is divided by x - a, then the remainder is equal to P(a). It provides a quick way to find the remainder of a polynomial division problem by evaluating the polynomial at the value of a. Examples are given to demonstrate evaluating polynomials using the remainder theorem.
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Long division can be used to divide polynomials in a similar way to dividing numbers. The key steps are to set up the division problem, divide the term of the dividend by the term of the divisor, multiply the divisor by the quotient term and subtract, then bring down the next term of the dividend and repeat. This polynomial long division allows polynomials to be factored by finding all divisor polynomials that give a remainder of zero. The factor theorem can also be used to check if a linear polynomial is a factor by setting it equal to zero and checking if it makes the other polynomial equal to zero.
5.3
This document discusses solving polynomial equations by factoring. It provides examples of factoring polynomials, including factoring the difference and sum of cubes. Factoring by substitution is also introduced as a method for factoring polynomials of degree 4 or higher. The document demonstrates solving polynomial equations by factoring the expressions and setting each factor equal to 0. Both real and imaginary solutions may be obtained depending on whether the factors are real or complex numbers. Graphing is presented as an alternative method to find real solutions of a polynomial equation.
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The document discusses inferences for correlation and regression. It provides an example of testing the correlation between percentage of population with a college degree (x) and percentage growth in income (y) for 6 Ohio communities. There is a positive correlation between x and y, but this does not necessarily mean higher education causes higher earnings. The document also discusses measuring the spread of data points around the least squares line, including the standard error of estimate, using an example of how much copper sulfate dissolves in water at different temperatures.
9.1 9.2 9.3 using the graph calc
This document provides guided notes on inferences for correlation and regression. It discusses how the sample correlation coefficient and least squares line estimate population parameters and require assumptions about the data. It also outlines how to test the population correlation coefficient using a significance test and interpret the results. An example is provided testing the correlation between education levels and income growth. Students are asked to practice computing the standard error of estimate from a data set and answering summary questions.
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1. The document discusses writing polynomials in factored form and finding the zeros of polynomial functions. It defines linear factors, roots, zeros, and x-intercepts as equivalent terms.
2. Examples are provided of writing polynomials in factored form using the factor theorem to find the zeros, and then graphing the polynomial function based on its zeros.
3. The factor theorem states that a linear expression x - a is a factor of a polynomial if and only if a is a zero of the related polynomial function. This allows writing a polynomial given its zeros.
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This document discusses how to describe the shape of a cubic function by listing it in standard form, describing the end behavior of the graph, determining the possible number of turning points using a table of values, and determining the increasing and decreasing intervals. It explains that to describe the shape, you identify the sign of the leading coefficient to determine the end behavior and the number of turning points, which is one less than the possible degree. The document also discusses using differences of consecutive y-values in a table to determine the least degree of the polynomial function that could generate the data, with constant first differences indicating linear, constant second differences indicating quadratic, and constant third differences indicating cubic.
5.1[1]
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9.2 lin reg coeff of det
1) Linear regression finds the "best-fitting" linear relationship between two variables by minimizing the vertical distances between the data points and the linear equation line.
2) The coefficient of determination, r^2, measures how well the linear relationship described by the regression line fits the actual data, with higher r^2 values indicating less unexplained variability.
3) r^2 has an interpretation as the percentage of the total variation in the response variable that is explained by the explanatory variable.
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8.2
- 1. P-VALUES
- 2. Review from 8.1 Summary of Hypothesis Testing •
- 3. •
- 4. •
- 5. Page 427 •
- 6. •
- 7. • Remember to find the P-value, you can use Table A or Normalcdf(1.08, E99)
- 8. •
- 9. •
- 10. •
- 11. •
- 12. Page 429 •
- 13. •
- 14. •
- 15. •