(a)
One-way ANOVA: Tensile Strength versus Mixing Technique
Source DF SS MS F P
Mixing Technique 3 121231 40410 8.22 0.002
Error 16 78619 4914
Total 19 199850
S = 70.10 R-Sq = 60.66% R-Sq(adj) = 53.28%
Individual 95% CIs For Mean Based on
Pooled StDev
Level N Mean StDev -----+---------+---------+---------+----
1 5 417.80 68.44 (------*-----)
2 5 473.80 83.29 (-----*------)
3 5 434.00 52.24 (-----*------)
4 5 615.40 72.83 (------*-----)
-----+---------+---------+---------+----
400 500 600 700
Pooled StDev = 70.10
Since p-value=0.002<0.05, so we conclude that mixing techniques affect the mean tensile strength of the cement.
(b)
Grouping Information Using Tukey Method
Mixing
Technique N Mean Grouping
4 5 615.40 A
2 5 473.80 B
3 5 434.00 B
1 5 417.80 B
Means that do not share a letter are significantly different.
Tukey 95% Simultaneous Confidence Intervals
All Pairwise Comparisons among Levels of Mixing Technique
Individual confidence level = 98.87%
Mixing Technique = 1 subtracted from:
Mixing
Technique Lower Center Upper
---------+---------+---------+---------+
2 -70.96 56.00 182.96 (-------*------)
3 -110.76 16.20 143.16 (-------*-------)
4 70.64 197.60 324.56 (-------*-------)
---------+---------+---------+---------+
-160 0 160 320
From above confidence intervals, we conclude that effect
of Mixing Technique 4 is significantly greater than effect of
Mixing Technique 1 (since the corresponding confidence interval
contains all positive values) and other mixing techniques are not
significantly different from 1 since the corresponding confidence
intervals contain zero.
Mixing Technique = 2 subtracted from:
Mixing
Technique Lower Center Upper
---------+---------+---------+---------+
3 -166.76 -39.80 87.16 (-------*------)
4 14.64 141.60 268.56 (-------*-------)
---------+---------+---------+---------+
-160 0 160 320
From above confidence intervals, we conclude that effect
of Mixing Technique 4 is significantly greater than effect of
Mixing Technique 2 (since the corresponding confidence interval
contains all positive values).
Mixing Technique = 3 subtracted from:
Mixing
Technique Lower Center Upper
---------+---------+---------+---------+
4 54.44 181.40 308.36 (-------*-------)
---------+---------+---------+---------+
-160 0 160 320
From above confidence intervals, we conclude that effect of Mixing Technique 4 is significantly greater than effect of Mixing Technique 3 (since the corresponding confidence interval contains all positive values).
Hence Mixing techniques 1,2 and 3 minimize the mean tensile strength.
Problem 2 Use Minitab for this problem The tensile strength of Portland cement is being studied....
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 1 Do this problem by hand - you may use Excel for calculations 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 1 324 448 364 654 4 504 485 422...
(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 (Ib/in) 3129 3200 2800 2600 3000 2865 3300 2975 29002985 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 observed...
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.
(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 (Ib/in2) 3129 3200 2800 2600 3000 2865 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...
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...
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...