The accompanying two-way table gives data for a 2 X 3 factorial experiment with two observations for each factor-level combination. Complete parts a through a. g Click the icon to View the data table. 0 Click the icon to View the ANOVAtable. Factorial Experiment Factor B 1 2 3 3.2, 4.1 4.7, 4.5 6.5, 7.2 5.7, 5.2 2.9, 2.3 34,2 5 a. Identify the treatments for this experiment. Calculate and plot the treatment means, using the response variable as the y-axis and the levels of factor B as the x-axis. Use the levels of factorA as plotting symbols. Do the treatment means appear to differ? Do the factors appear to interact? Identify the treatments for this experiment. Choose the Correct answer below, , There are 6 treatments. Each treatment consists of one of the 2 levels of the first factor combined With one of the 3 levels of the second factor, . There are 3 treatments. Each treatment consists of one of the 3 levels of the second factor combined with the 3 levels of the second factor. . There are 12 treatments. Each treatment consists of one of the 2 levels of the rst factor combined with one of the 3 levels of the second factor, and there are 2 observations for each factor-level combination. . There are 2 treatments. Each treatment consists of one of the 2 levels of the first factor combined with the 3 levels of the second factor. The accompanying two-way table gives data for a 2 x 3 factorial experiment with two observations for each factor-level combination. Complete parts a through e. g Click the icon to View the data table. 0 Click the icon to view the ANOVA table. C) D. There are 2 treatments, Each treatment consists of one of the 2 levels of the first factor combined with the 3 levels of the second factor. Calculate the treatment means. Let ;U be the mean for the treatment consisting of level i of factorAand level j of factor B. for l = 1,2 and j = 1.23. X11: X12: X13: X21 : X22 : x23 : (Type integers or decimals.) Plot the treatment means using the key shown to the right. Choose the correct graph below. ' Level 1, FactorA - - Level 2, FectorA C) A. Q B. U c. Cl D. 1 Q i 2 1 a Q i Q 3 o 8 8 l 8 g , _r ' Q E * x I a Q E Q c .- _,.. . = c '0 ' : a 2' ' a E m o o 1 z 3 1 2 3 Factor B Factor B Faclor E Do the treatment means appear to differ? Do the factors appear to interact? The accompanying two-way table gives data for a 2 x 3 factorial experiment with two observations for each factor-level combination. Complete parts a through e. g Click the icon to view the data table. a Click the icon to View the ANOVA table. Do the factors appear to interact? Ves b. The ANOVA table for this experiment is now shown in the problem statement, Test to determine whether the treatment means differ at the (x = 0.05 level of significance. Does the test support your visual interpretation from part a? State the null and alternative hypotheses. Ho: v Ha: v Find the test statistic, F = (Round to two decimal places as needed.) Find the p-value. p-value = (Round to three decimal places as needed.) Does the test support your visual interpretation from part a? V V H0, The data V sufcient evidence that at least two of the treatment means differ at (x = 0.05. which V the visual interpretation from part a, C. Does the result of the test in part b warrant a test for interaction between the two factors? If so. perform it, using a = 0.05. If warranted, state the null and alternative hypotheses. Choose the correct answer below. C! A. He: FactorsAand B do interact to affect the response mean, The accompanying two-way table gives data for a 2 x 3 factorial experiment with two observations for each factor-level combination. Complete parts a through e. g Click the icon to view the data table. 0 Click the icon to view the ANOVA table. If warranted, state the null and alternative hypotheses. Choose the correct answer below. Ho: FactorsAand B do interact to affect the response mean. : At least two treatment means differ. Ho: No differences exist among the b mean levels of factor B, Ha: No differences exist among the a mean levels of factorA. .0 I o : Factors A and B do not interact to affect the response mean, Ha: FactorsAand B do interact to affect the response mean. l; D. Atest for interaction between the two factors is not warranted, If warranted, find the test statistic, Select the correct choice below and, if necessary, ll in the answer box to complete your choice. 1" Atest for interaction between the two factors is warranted, The test statistic is F = (Round to two decimal places as needed.) \\.:.I' B. Atest for interaction between the two factors is not warranted. If warranted, find the p-value. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. '3' A- A test for interaction between the two factors is warranted, The p-value is (Round to three decimal places as needed.) B. Atest for interaction between the two factors is not warranted. |f warranted. make an appropriate conclusion for the test. Choose the correct answer below, The accompanying two-way table gives data for a 2 X 3 factorial experiment with two obsen/ations for each factor-level combination. Complete parts a through 9 E Click the icon to view the data table. 0 Click the icon to view the ANOVA table. If warranted. make an appropriate conclusion for the test. Choose the correct answer below. C} A. Reject H0, The data provide sufficient evidence of an interaction effect upon the response for these two factors at (x = 0,05, Reject H0, The data do not provide sufficient evidence of an interaction effect upon the response for these two factors at (x = 0.05. {7' C. Do not reject Ho. The data provide sufficient evidence of an interaction effect upon the response for these two factors at ix = 0.05. {7 D. Do not reject HO' The data do not provide sufficient evidence of an interaction effect upon the response for these two factors at (1 =0.05. '1" E. The test was not performed because it was not warranted. d. Do the results of the previous tests warrant tests of the two factor main effects? if so, perform them, using or = 0.05. If warranted, state the null and alternative hypotheses for testing the main effect of factor A, Choose the correct answer below. i" A. H0: No differences exist among the a mean levels of factor A, : At least two factorA mean levels differ. {:3 B. H0: FactorsAand B do interact to affect the response mean. t least two factorA mean levels differ. H0: No differences exist among the b mean levels of factor B. Ha: At least two treatment means differ D. Tests for the two factor main effects are not warranted. If warranted. find the test statistic for testing the main effect of factor A, Select the correct choice below and. if necessary, fill in the answer box to complete your choice, A- Tests of the two factor main effects are warranted, The test statistic for testing the main effect of factor A is F(A) : IRmInd tn mm decimal nianee ae needed \\ The accompanying twoway table gives data for a 2 x 3 factorial experiment with two observations for each factor-level combination. Complete parts a through e. E Click the icon to view the data table. 0 Click the icon to view the ANOVA table. (I) If warranted, find the test statistic for testing the main effect of factor A. Select the correct choice below and, if necessary. ll in the answer box to complete your choice. Ci A- Tests of the two factor main effects are warranted. The test statistic for testing the main effect of factor A is F(A) = (Round to two decimal places as needed ) C B. Tests of the two factor main effects are not warranted. If warranted, find the p-value for testing the main effect of factorA. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. ':3 A- Tests of the two factor main effects are warranted. The p-value for testing the main effect of factorA is (Round to three decimal places as needed.) Q B. Tests of the two factor main effects are not warranted. If warranted, make an appropriate conclusion for the test. Choose the correct answer below, Reiect H0 The data do not provide sufficient evidence that at least two of the factor A mean levels differ. C B. Do not reject H0. The data provide sufficient evidence that at least two of the factor A mean levels differ. C3 C. Do not reject H0. The data do not provide sufficient evidence that at least two of the factorA mean levels differ. Cl D. Reject H0, The data provide sufficient evidence that at least two of the factorA mean levels differ l:i E. The test was not performed because it was not warranted. If warranted, state the null and alternative hypotheses for testing the main effect of factor B. Choose the correct answer below. [3 A. He: No differences exist among the b mean levels of factor B. Ha: At least two factor B mean levels differ, The accompanying two-way table gives data for a 2 x 3 factorial experiment With two observations for each factor-level combination, Complete par1s a through 9. @ Click the icon to View the data table. Click the icon to View the ANOVAtable, if warranted. state the null and alternative hypotheses for testing the main effect of factor B. Choose the correct answer below : No differences exist among the b mean levels of factor B. : At least two factor B mean levels differ, : At least two factorA mean levels differ. : No differences exist among the in mean levels of factor B. : Factors A and B do not interact to affect the response mean. : At least two treatment means differ. . Tests for the two factor main effects are not warranted. if warranted, nd the test statistic for testing the main effect of factor B. Select the correct choice below and, if necessary, ll in the answer box to complete your choice. A. Tests of the two factor main effects are warranted. The test statistic for testing the main effect of factor B is F(B) = (Round to two decimal places as needed.) B. Tests of the two factor main effects are not warranted if warranted, find the p-value for testing the main effect of factor B. Select the correct choice below and. if necessary, fill in the answer box to complete your choice. A- Tests of the two factor main effects are warranted. The pva|ue for testing the main effect of factor B is (Round to three decimal places as needed.) B. Tests of the two factor main effects are not warranted if warranted, make an appropriate conclusion for this test, Choose the correct answer below. nR M. MA u TL'A 4-... \"more \"Mm...\" whom\". a... .. in... a...\" \"nu\" ;.....~ :- MM i......r,. 4mm The accompanying two-way table gives data for a 2 x 3 factorial experiment with two observations for each factor-level combination. Complete parts a through e. g Click the icon to view the data table, Click the icon to view the ANOVA table. (Round to two decimal places as needed.) \\i' B. Tests of the two factor main effects are not warranted If warranted, find the p-value for testing the main effect of factor B. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. '3 A- Tests of the two factor main effects are warranted. The p-velue for testing the main effect of factor B is (Round to three decimal places as needed.) . B. Tests of the two factor main effects are not warranted If warranted, make an appropriate conclusion for this lest. Choose the correct answer below. Cl A. Do not reject H0, The data provide sufficient evidence that at least two of the factor B mean levels differ, (:l B. Reject H0. The data do not provide sufficient evidence that at least two of the factor B mean levels differ. l) C. Reject H0. The data provide sufficient evidence that at least two of the factor B mean levels differ. C D. Do not reject H0, The data do not provide sufficient evidence that at least two of the factor B mean levels differ. Ci E. The test was not performed because it was not warranted, e. Interpret the results of the tests. Do they support your visual interpretation from part a? Q A. Only the results of the test from part c agree with the interpretation from part a, Q B. Only the results of the tests from part d agree With the interpretation from part a. Q C. None of the results of the tests agree with the interpretation from part a. Cl D. The results of all the tests agree with the interpretation from part a