Question 12.20 – Use these data - incidents of reports of underage drinking – to perform the following: “Dry” campus, state school: 47, 52, 27, 50 “Dry” campus, private school: 25, 33, 31 “Wet” campus, state school: 77, 61, 55, 48 “Wet” campus, private school: 52, 68, 60

a.) Calculate the cell and marginal means. Notice the unequal Ns b.) Draw a bar graph. c.) Calculate the five different degrees of freedom, and indicate the critical F value based on each set of degrees of freedom, assuming the p level is 0.05. d.) Calculate the total sum of squares. e.) Calculate the between-groups sum of squares of the independent variable campus. f.) Calculate the between-groups sum of squares for the independent variable school. g.) Calculate the within-groups sum of squares. h.) Calculate the sum of squares for the interaction. i.) Create a source table.

Prove the following by induction: 2 + 4 + 6 + …+ 2n = n(n+1) for all integers n

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Find the intersection point (if any) of the lines r1(t)=(17,54,−22)+t(−3,−8,3)r1(t)=(17,54,−22)+t(−3,−8,3) and r2(s)=(−67,−50,37)+s(12,8,−7)r2(s)=(−67,−50,37)+s(12,8,−7).

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Which is the most accurate method of the decomposition methods used for the following data set.
Additive with seasonal only, Additive with trend plus seasonal , Multiplicative with seasonal only ,Multiplicative with trend plus seasonal

Sum An a series and |An| cnverges to 0. If the partial sum Sn (A1+A2+...+An) is bounded, is the partial sum Sn' of all absolute value of An (|A1|+|A2|+...+|An|) also bounded?

Solve this differential equation

(4x - 2y)dx + (2x - 9y)dy = 0

1)What is the advantage of solving differential equations using Laplace Transforms over prior time-domain techniques cover thus far this semester (Chps 1-5)?

2) When using Laplace Transforms, what is the difference in the notation between lower case (i.e. f(t)) and upper case (i.e. F(s)) letters?

3) If the Laplace Transform is an integral as shown in Sec 7.1, pg 438, equation #1, how can Dr. Tran claim that the Laplace Transform technique does not require use of Calculus? Is he crazy? Please explain.

2. The MCAT, Medical College Admissions Test, must be taken by students wishing to gain entrance to most Medical Programs in Canada and the United States. There are four sections: Physical Sciences (PS), Verbal Reasoning (VR), Biological Sciences (BS), and Writing Sample (WS). The first three are each scored on a scale from 1 to 15, with a mean of 8 and a standard deviation of 2.

(a) Determine the percentile ranks for the following students:

(b) If a Medical School sets a requirement that students who will be considered must have a score of 10 on the Physical Science, 12 on the Verbal Reasoning and 11 on the Biological Sciences sections, what proportion of the population will qualify for each portion of the test?

c) The ACT, American Colleges Test, is comparable to the SAT Reasoning Test. The ACT is well modeled by a normal distribution, X~ N(21, 52 ), whereas the SAT Reasoning Test is modeled by S~N(1500, 3002 ). A college will accept either the SAT or the ACT for admissions. A college admissions assistant needs to compare the following two students to each other though they wrote different tests. How would the admissions assistant do this? Which student seemed to score better? Matthew Chant ACT Score = 27 Joseph Bell SAT Score = 2050

What extensions to other mathematics and real world applications does Group Cohomology have?

Choose your favorite unique vector b in R³ with no 0 entries.

8. What is your vector b?
9. Based on the “Equivalent Conditions for a Non-Singular Matrix” on page 123 in our text, why must Ax = b have a unique solution in this situation?

10. Solve the equation Ax = b the following three ways (you should get the same answer each way!) Recall – calculator OK, in fact suggested. (24 points – 8 points each)
    • Solve the equation Ax = b using Gaussian Elimination. Show the augmented matrix and then use “ref” or “rref” on your calculator. Complete with back substitution.
    • Solve the equation Ax = b using the inverse of (A), which you have already calculated above.
    • Solve the equation Ax = b using Cramer’s Rule. Identify A, A_x, A_y, A_z and their determinants.
11. Express b as a linear combination of the column vectors of A.

12. In practice involving very large systems with square matrices of coefficients, Gaussian Elimination is often implemented by using LU factorization. Why do you think that is the case? 10-20 words (more if you want).

Replace the first row of your matrix A with the second row of your matrix A. Call this new 3x3 matrix with 2 equal rows B.

13. What is your matrix B?

14. Calculate the determinant of B without a calculator. Perform at least one row or column operation on the Determinant as part of your calculation procedure.

15. Solve the Matrix equation Bx =0

• What is the general solution for x in terms of (say) any real number t?
• Determine a specific non-zero solution for x (I.e. assign t to a specific real number)?
• Verify that Bx = 0 for your specific solution for x.