An experiment was conducted to investigate the effect of four factors-temperature T₁, pressure P, catalyst C, and temperature T₂-on the yield Y of a chemical. (a) The values (or levels) of the four factors used in the experiment are shown in the accompanying table. T1 x1 P X2 C×3 2 ×4 50 -1 10 -1 1 -1 100 -1 70 1 20 1 2 1 200 1 If each of the four factors is coded to produce the four variables X1, X2, X3, and x4, respectively, give the transformation relating each coded variable to its corresponding original. О Each transformation is defined, for each factor, by subtracting the midpoint (the mean) and dividing by one-half the range. Each transformation is defined, for each factor, by subtracting the midpoint (the mean) and multiplying by twice the range. Each transformation is defined, for each factor, by subtracting the midpoint (the mean) and multiplying by one-half the range. Each transformation is defined, for each factor, by subtracting the midpoint (the mean) and dividing by twice the range. (b) Consider the data set. +1 x4 -1 X3 X3 -1 1 -1 1 -1 22.3 24.5 24.5 25.9 -1 x2 5 1 19.4 24.0 25.3 28.4 -1 22.1 19.6 23.5 16.6 +1 x2 1 14.3 12.7 19.3 16.0 Fit the linear model Y = B0 + B1x1 + ẞ2x2 + ẞ3x3 + ẞ4×4 + ε to the data. (Round your answers to four decimal places.) Y = ] )x3 + + (c) Do the data present sufficient evidence to indicate that T₁ contributes information for the estimation of Y? Does P? Does C? Does T2? (Test the hypotheses, respectively, that ẞ₁ = 0, ß₂ = 0, ß3 = 0, and ẞ4 = 0.) What would you conclude if you used a = 0.01 in each case? State the null and alternative hypotheses for i = 1,...,4. Ho B₁ = 0 Ha: Bi > 0 Ho=0 H₂ P < 0 = Ho-0 H₂: B₁ = 0 Ho: B₁ = 0 H₂ B₁ = 0 Ho: Bi > 0 Ha B₁ = 0 Give the value of the test statistic to test whether the data present sufficient evidence to indicate that T₁ contributes information for the estimation of Y. (Round your answer to three decimal places.) T = Give bounds for the associated p-value. O 0.200 > p-value 0.1 < p-value < 0.2 0.05 < p-value < 0.1 0.02 < p-value < 0.05 0.01 < p-value < 0.02 p-value < 0.01 What is the conclusion of your test? Reject Ho. The data do present sufficient evidence to indicate that T₁ contributes information for the estimation of Y. Reject Ho. The data do not present sufficient evidence to indicate that T₁ contributes information for the estimation of Y. Fail to reject Ho. The data do not present sufficient evidence to indicate that T₁ contributes information for the estimation of Y. Fail to reject Ho. The data do not present sufficient evidence to indicate that T₁ contributes information for the estimation of Y. Give the value of the test statistic to test whether the data present sufficient evidence to indicate that P contributes information for the estimation of Y. (Round your answer to three decimal places.) T = Give bounds for the associated p-value. 0.200 > p-value O 0.1 < p-value < 0.2 0.05 < p-value < 0.1 0.02 < p-value < 0.05 0.01 < p-value < 0.02 O p-value <0.01 What is the conclusion of your test? ◇ Fail to reject Ho. The data do not present sufficient evidence to indicate that P contributes information for the estimation of Y. Fail to reject Ho. The data do not present sufficient evidence to indicate that P contributes information for the estimation of Y. Reject Ho. The data do present sufficient evidence to indicate that P contributes information for the estimation of Y. Reject Ho. The data do not present sufficient evidence to indicate that P contributes information for the estimation of Y. Give the value of the test statistic to test whether the data present sufficient evidence to indicate that C contributes information for the estimation of Y. (Round your answer to three decimal places.) T = Give bounds for the associated p-value. 0.200 > p-value 0.1 < p-value <0.2 0.05 < p-value < 0.1 0.02 < p-value < 0.05 0.01 < p-value < 0.02 O p-value < 0.01 What is the conclusion of your test? Fail to reject Ho. The data do not present sufficient evidence to indicate that C contributes information for the estimation of Y. Fail to reject Ho. The data do not present sufficient evidence to indicate that C contributes information for the estimation of Y. Reject Ho. The data do present sufficient evidence to indicate that C contributes information for the estimation of Y. Reject Ho. The data do not present sufficient evidence to indicate that C contributes information for the estimation of Y. Give the value of the test statistic to test whether the data present sufficient evidence to indicate that T₂ contributes information for the estimation of Y. (Round your answer to three decimal places.) T = Give bounds for the associated p-value. 0.200 p-value O 0.1 <p-value < 0.2 0.05 <p-value < 0.1 0.02 < p-value < 0.05 0.01 < p-value < 0.02 O p-value < 0.01 What is the conclusion of your test? Reject Ho. The data do not present sufficient evidence to indicate that T₂ contributes information for the estimation of Y. Reject Ho. The data do present sufficient evidence to indicate that 72 contributes information for the estimation of Y. Fail to reject Ho. The data do not present sufficient evidence to indicate that T2 contributes information for the estimation of Y. Fail to reject Ho. The data do not present sufficient evidence to indicate that T₂ contributes information for the estimation of Y.