Prove that the reduced row echelon forms of the matrices
are the two matrices.
The point of the reduced row echelon form is that the corresponding system of linear equations is in a particularly simple form, from which the solutions to the system
The article “Anodic Fenton Treatment of Treflan MTF” describes a two-factor experiment designed to study the sorption of the herbicide trifluralin. The factors are the initial trifluralin concentration and the \(\displaystyle{F}{e}^{{{2}}}\ :\ {H}_{{{2}}}\ {O}_{{{2}}}\) delivery ratio. There were three replications for each treatment. The results presented in the following table are consistent with the means and standard deviations reported in the article. \(\begin{array}{|c|c|}\hline \text{Initial Concentration (M)} & \text{Delivery Ratio} & \text{Sorption (%)} \\ \hline 15 & 1:0 & 10.90 \quad 8.47 \quad 12.43 \\ \hline 15 & 1:1 & 3.33 \quad 2.40 \quad 2.67 \\ \hline 15 & 1:5 & 0.79 \quad 0.76 \quad 0.84 \\ \hline 15 & 1:10 & 0.54 \quad 0.69 \quad 0.57 \\ \hline 40 & 1:0 & 6.84 \quad 7.68 \quad 6.79 \\ \hline 40 & 1:1 & 1.72 \quad 1.55 \quad 1.82 \\ \hline 40 & 1:5 & 0.68 \quad 0.83 \quad 0.89 \\ \hline 40 & 1:10 & 0.58 \quad 1.13 \quad 1.28 \\ \hline 100 & 1:0 & 6.61 \quad 6.66 \quad 7.43 \\ \hline 100 & 1:1 & 1.25 \quad 1.46 \quad 1.49 \\ \hline 100 & 1:5 & 1.17 \quad 1.27 \quad 1.16 \\ \hline 100 & 1:10 & 0.93 \quad 0.67 \quad 0.80\\ \hline \end{array}\) a) Estimate all main effects and interactions. b) Construct an ANOVA table. You may give ranges for the P-values. c) Is the additive model plausible? Provide the value of the test statistic, its null distribution, and the P-value.
Response rates to Web surveys are typically low, partially due to users starting but not finishing the survey. The factors that influence response rates were investigated in Survey Methodology (Dec. 2013). In a designed study, Web users were directed to participate in one of several surveys with different formats. For example, one format utilized a welcome screen witb a white background, and another format utilized a welcome screen with a red background. The "break-off rates," i.e., the proportion of sampled users who break off the survey before completing all questions, for the two formats are provided in the table.
a) Verify the values of the break-off rates shown in the table.
b) The researchers theorize that the true break-off rate for Web users of the red welcome screen will be lower than the corresponding break-off Tate for users of the white welcome screen. Give the null and alternative hypotbesis for testing this theory.
c) Conduct the test, part b, at
In a similar study using the same design (sample of
The average number who said they noticed was (population mean) 3.1. Calculate a One Sample t-test using a two-tailed test with