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 4) or variability in different batches (factor 8). Each number is a cell total (x,y) based on K = 3 observations. Batch 3 2 5 1935 1 1846 1778 1804 1 2 3 Capping Material 4 1888 1785 1892 1941 1850 1892 1792 1890 1799 1626 1757 In addition, LEDx2 = 16,810,777 and 22x2 = 50,418,409. The hypotheses are as follows: Hogi og = 0 Hoe: 0 = 0 Han: at least one x = 0 Ho Obtain the ANOVA table and then test at level 0.01 the hypotheses Hog versus H G Hversus Hr and Hoe versus 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 A 4 8 AB Error 18 30 ✓ Total 44 Test for an interaction. Find the critical value. (Round your answer to two decimal places.) F. State the conclusion in the problem context. Fail to reject Hog. The data does not suggest that there is an interaction. Reject HOG. The data suggests that there is an interaction. O Reject HOG. The data does not suggest that there is an interaction. O 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.) = State the conclusion in the problem context. Reject H. The data suggests that there is a capping effect. O Fail to reject Hoa: The data does not suggest that there is a capping effect. O Reject HQAThe 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.) Fav.v2 = 1 State the conclusion in the problem context. Reject Haa: The data does not suggest that there is a batch effect. O Fail to reject Hoe. 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 Haa: The data suggests that there is a batch effect.

Answer 1

Testing by pothesis as follows, HOG: 82o & Hage : rexo HOA : 2 = 422 43=0 Vs Ha A: at least one di to HOB: 0/220 V HaB: 870.

let the data as, Capping Mcelerial (factor A) 1 Batch Total (factor B) 3 4 5 1846 1941 1935 1888 1199 1448 1850 92 1785 1626 1804 1892 1890 1892 1757 9235. 5428 5683 5617 55655182 G= 27475 g4og 883) 3 Total ( Bj) {EExijke 1 - 16810717 = 50418409 {exy? m-3 k=3, h=5. N = mih z 45 C.F= (274752 = 16775013.89 N R.S.S - Ess xy 10L = 16810777 7-SS= R.S.S - Cf z 16810787 - 16745013.89 T.S.S= 35763.11 S-SA= S.S. due to Factor A ( capping ( Capping material ET;.2 mh 0409)2+(883)2 + (9235)2 - 16745013.89 15

SSA=117239) s.s. due to factor B (Batch) S.S.BE ΣΒ2 -of mk (5428) ²+ (568934 (56141²+ (5565)2+ (51822 9 16795013,89 ISSB 17509.56 3.s due to interacth AB. SSAB= ECXij? cfr-SSA- SSB 5041840g 3 16775013.89 1723.91 – 17509.56 SS AB = 1888.98 S.S.E T.S.S - S.SA-SSB- SSAB - 35763.11- 11723.91-17509, 56- 1888.98 S.S. E= 4640.67

ANOVA Tables Source df R SS (3) MS (41=(3)? a) A 2 11723.9) 5861.96 37.89 B 4 1509.56 4877.39 28.29 AB 8 1888.98 236.12 1.53 Emor 30 4640.67 154.69 Total 44 35763.11 Test for interaeth tem, antical f at 220.054 dt z (810) Foor, 8130= 2,27. fail to reject Hoce. The data does not suggest that there is an interaeth Test for a Capping effect. Foros, 2,30 = 3.32 Reject Hop. The data suggest that there is

a Cupping effect Testing for a Batch eftech foros, 4.30 = 2.69 Reject Hog. The data suggests that there is a batch effect