Question

The accompanying data was obtained in an experiment to investigate whether compressive strength of concrete cylinders depends on the type of capping material used (factor A) or variability in different batches (factor 8). Each number is a cell total (x,y) based on K = 3 observations. 1 1 1846 1778 1804 2 1941 1850 Batch 3 1935 1792 1890 4 1889 1785 1892 5 1799 1626 1757 Capping Material 2 3 1892 In addition, EDX 2 = 16,810,777 and 2x 2 = 50,418,409. The hypotheses are as follows: Hog! 062 = 0 Hoa, - = a= 0 Hog: 0,2 = 0 HAG: 0,2 > 0 H.A at least one x = 0 Haglog > 0 Obtain the ANOVA table and then test at level 0.01 the hypotheses Hoe versus Hr Honversus Hr and Hversus Hr assuming that capping is a fixed effect and batches is a random effect. (Round your answers to two decimal places.) Source df SS MS f 11723.91 5861.96 X 17509.56 4377 39 28.29 x AB 1888.98 236.12 1.53 Error 30 4840.87 154.69 Tota 44 35783.11 A 2 37.89 8 Test for an interaction. Find the critical value. (Round your answer to two decimal places.) = 2.27 X State the conclusion in the problem context. Fail to reject Hog. The data does not suggest that there is an interaction. Reject Hac. The data suggests that there is an interaction. O Reject Hoc. The data does not suggest that there is an interaction. Fail to reject Hog. The data suggests that there is an interaction. Test for a capping effect. Find the critical value. (Round your answer to two decimal places.) Favy> -3.32 1x State the conclusion in the problem context. Reject Ho. The data suggests that there is a capping effect. O Fail to reject Ho. The data does not suggest that there is a capping effect. Reject HaA. The data does not suggest that there is a capping effect. O Fail to reject Hox: The data suggests that there is a capping effect. Test for a batch effect. Find the critical value. (Round your answer to two decimal places.) = 2.69 Jx Fast State the conclusion in the problem context. Reject Hoa. The data does not suggest that there is a batch effect. O Fail to reject Hug. The data does not suggest that there is a batch effect. Fail to reject Ho. The data suggests that there is a batch effect. Reject Hon. The data suggests that there is a batch effect.

Answer 1

MS of A 586). 96 37.8948 f value for A 11 MS of Error 154.69 ~ 37.90 .: F value for A= 37.go f value for B 4377.39 154.69 MS of B Ms of Error - 28.2978 ň 28.30 f value for 28.30 Test for an Fr, 0,02 interaction :- (AB) Sir= 0.01 Foro, 8,30 , = d.f. of AB=8 92= d.f. of Error = 30 = FINV(0.01,8,30) = 13.17 { Using MS-Excel ? is an a L=oool Vi= d.f. of A = 2 - Fool,2,30 = FINV (0.01,2,30 ) = 15.39 o fail to reject Hog, The data does not suggest that there intrachion. F < Fr, 0,02 fed i.e, 1-53 <3.17, fail to reject Hog fail to reject Hos} Test for capping effect :-(A) Fa, V, 102 Va a dif. of Error = 30} { Using Ms-Excel} data suggest that there is Capping effect Test for batch effect :-(B) 9420.00, di Edif. of B=4 ? V2 =d. f. of Errono = FIND (0001, 4,30) = 16.02 { using Ms. Excel } Reject HOB data suggests that there is a batch effect. { : F7FX f> Fx, 0,02 1., 28.2974.02 Reject Reject HOA The C a Fr, 0,02 Foool, 4,30 The HOB