1.Here the response is tensile strength measurements.
factor is mixing technique
there are four levels of factor.
there are no replications.
null hypothesis,H0:tow1=tow2=tow3=tow4 i.e,the treatment or factor effects are same.
alternative hypothesis,H1:At least two of towi's are different,i=1(1)4.
Raw S.S(R.S.S)=(324^2)+(461^2)+...+(538^2).=4909201
Grand Total(G)=324+...+538=9705
Correction Factor(C.F)=(G^2)/n=(G^2)/20=4709351.25,where n is total number of plots=4*5=20
Total S.S(T.S.S)=R.S.S-C.F=199849.75
Treatment S.S.=(((T1^2)+...+(T4^2))/5)-C.F=(24152911/5)-4709351.25=121230.95
[T1,T2,T3,T4 are treatment totals of treatment 1,2,3,4,such that
T1=2089,T2=2369,T3=2170,T4=3079]
Error S.S=Total S.S-Treatment S.S=78618.8
SOURCE OF VARIATION |
S.S | d.f | M.S.S=S.S/d.f | variation ratio,'F' |
TREATMENTS | 121230.95 | 3 | 40410.32 | |
ERROR | 78618.8 | 16 | 4913.68 | |
TOTAL | 199849.75 | 19 | 45324 |
VARIATION RATIO 'F'=40410.32/4913.68=8.22
from f- distribution table,F0.05(3,16)=3.06
THUS 'F'>F0.05(3,16),THUS H0 is rejectedat 5%level of significance
thus mixing techniques affect the mean tensile strength of cement
Problem 1 Do this problem by hand - you may use Excel for calculations The tensile...
The tensile strength of Portland cement is being studied. Several different mixing techniques can be used economically A completely randomized experiment is conducted to determine if mixing technique has a significant effect on the mean tensile strength of cement. Several measurements of tensile strength are recorded (see table below) for each mixing technique Tensile Strength (lb/in2) measurements Mixing Technique 1 2 324 448 364 654 461 467 465 537 402 600 502 655 4 504 485 422 693 5 398...
Problem 2 Use Minitab for this problem The tensile strength of Portland cement is being studied. Several different mixing techniques can be used economically. A completely randomized experiment is conducted to determine if mixing technique has a significant effect on the mean tensile strength of cement. Several measurements of tensile strength are recorded (see table below) for each mixing technique. Tensile Strength (lb/in2) measurements Mixing Technique 1 324 448 364 654 461 467 465 537 4 504 485 422 693...
3. The tensile strength of Portland cement is being studied. Four different mixing techniques can be used economically. A completely randomized experiment was conducted and the following data were collected Mixing Technique Tensile Strength (lb/in2) 3129 3200 2800 2600 3000 2865 3300 2975 2900 2985 2700 2600 2890 3150 3050 2765 4 (a) Test the hypothesis that mixing techniques affect the strength of the cement. State the model, hypotheses, test statistic, decision rule, ANOVA table and decision clearly
3. The tensile strength of Portland cement is being studied. Four different mixing techniques can be used economically. A completely randomized experiment was conducted and the following data were collected Mixing Technique Tensile Strength (lb/in2) 3129 3200 2800 2600 3000 2865 3300 2975 2900 2985 2700 2600 2890 3150 3050 2765 (a) Test the hypothesis that mixing techniques affect the strength of the cement. State the model, hypotheses, test statistic, decision rule, ANOVA table and decision clearly.
Use of any computer software is not allowed. Solve the following problems using calculator and probability tables. Show all computations 3. The tensile strength of Portland cement is being studied. Four different mixing techniques can be used economically. A completely randomized experiment was conducted and the following data were collected. Mixing Technique Tensile Strength (Ib/in') 3129 3000 2865 3200 3300 2975 2800 2900 2985 2600 2700 2600 2890 3150 3050 2765 (a) Test the hypothesis that mixing techniques affect the...
1. (Continuation of the Portland cement data) The tensile strength of Portland cement is being studied Four different mixing techniques can be used economically. A completely randomized experiment was conducted and the following data were collected Mixing Technique Tensile Strength (lb/in) 3129 3200 2800 2600 3000 2865 3300 2975 2900 2985 2700 2600 2890 3150 3050 2765 (a) Calculate the standardized residuals of the ANOVA model and calculate the theoretical normal quantiles. Make a table of theoretical normal quantiles vs...
1. (Continuation of the Portland cement data) The tensile strength of Portland cement is being studied Four different mixing techniques can be used economically. A completely randomized experiment was conducted and the following data were collected Mixing Technique Tensile Strength (lb/in2) 3129 3200 2800 2600 30002865 3300 2975 2900 2985 2700 2600 2890 3150 3050 2765 4 (a) Calculate the standardized residuals of the ANOVA model and calculate the theoretical normal quantiles. Make a table of theoretical normal quantiles vs...
3. The tensile strength of Portland cement is being studied. Four different mixing techniques can be used economically. The following data have been collected: Technique Tensile strength 3129 3000 2865 2890 3200 3300 2975 3150 2800 2900 2985 3050 2600 2700 2600 2765 3 and can be read into R with the commands: y c(3129, 3000, 2865, 2890, 3200, 3300 , 2975, 3150, 2800, 2900, 2985, 3050 2600 , 2700 , 2600 2765 x = c(rep(1,4),rep (2,4),rep (3,4),rep(4,4)) Test the...