[4] Use Gaussian elimination with back substitution to solve the linear system of equations x2 + x3 4x1 2x1 + 5x2 + 2x3 x1 + 2x₂ + 4x3 = = = 8 3 11

Please do not give solution in image format thanku

Solve using a. Gaussian elimination and b. Gauss Jordan elimination methods 2x₁ + 6x2 + x3 = 7 X₁ + 2x2 - x3 = -1 5x₁ + 7x2 - 4x3 = 9

Q8 A desk lamp produced by DavidLee Company was found to be defective (D). There are three factories (A, B, C) where such desk lamps are manufactured. A Quality Control Manager (QCM) is responsible for investigating the source of found defects. This is what the QCM knows about the company's desk lamp production and the possible source of defects: Factory A B с % of Total Production 25%, or P(A) = 0.25 35%, or P(B) = 0.35 40%, or P(C)=0.40 % of defective 3.5%, or P(D/A) =0.035 4.5%, or P(D/B) = 0.045 6.5%, or P(D/C) = 0.065 If 100 products are randomly selected from these three factories, how many defects will be found?

Part A

RABCD X₁ 12 20 2 A researcher is interested in seeing if listening to a political debate changes anxiety scores among people. The researcher knows of no previous research that would predict whether anxiety scores would be raised or lowered. The researcher gathers a sample of n = 4, and gives these participants an anxiety test before and after listening to the political debate. Below are the data (anxiety scores) at time one (X₁) and time two (X₂) for all participants. Participant 10 10 X₂ 28 24 26 18 b.) Is this a one or a two-tailed test? a.) State the researcher's null and alternative hypotheses (using symbols OR everyday language): c.) Find the critical value (alpha = .05) d.) Compute the observed test statistic (remember to show your work) 5 e.) Based on the information above, what is your statistical conclusion? f.) Describe briefly what we can conclude in practical terms 6 g.) Based on the results above, calculate a Cohen's d and interpret what this tells us about the difference…