D. Glass phase
2. Amount of Glass required for vitrification
The glass is arguably the most important component of a porcelain body. Since it represents more than 50% of the microstructure, the physical properties of the body such as CTE, true density, and elastic modulus are potentially dominated by the properties of the glass phase.33 There is also a certain amount of glass necessary to densify the body and eliminate the open porosity. While it has already been established that the time required for densification at a given temperature increases with decreasing flux level (Figure 5), the data indicate that the amount of glass necessary for densification increases with increasing flux level via the following equation:
ρG = 2.296 + 0.016*[R2O+RO]
39
𝐺𝑙𝑎𝑠𝑠 (𝑤𝑡%) = 39.49 + 3.13 ∗ (𝑅2𝑂 + 𝑅𝑂 ) + 2.80 ∗ 𝐿𝑜𝑔(𝑡) (8) Where the weight percent of glass (Glass) is a function of the flux content, (R2O+RO) on a mole % basis, and the dwell time (t, hours), at the densification temperature.
When the alkali level increases, as is now becoming more commonplace in industry (i.e, increasing the 25% feldspar level in traditional recipes to 30 or 35%), the model accurately predicts a higher glass content necessary for densification. This is reasonable, however, because increasing the feldspar level is accomplished at the expense of clay and quartz, and thus reduces the crystalline content of the fired body. The results of this model are presented as a contour plot of flux level in Figure 21. A comparison between predicted and measured glass levels, for bodies fired properly to achieve the 0.2% water absorption target, is shown in Figure 22.
Dwell time (hr)
0.1 1
Amount of glass necesary for densification (Weight%)
48 50 52 54 56 58 60 62 64
8
8
8
8
7
7
7
7
6 6
6 6
5 5
5 5
4
4
4
4
3 3
3 3
Figure 21. Amount of glass necessary for vitrification as a function of dwell time and flux level (mole %) when the body is fired at the proper maturation temperature.
40
Measured amount of Glass (%WB)
50 52 54 56 58 60 62 64
Calculated amount of glass (%WB)
50 52 54 56 58 60 62 64
0.10 hr 0.32 hr 1.00 hr Regr
99% Conf. Int.
Figure 22. Comparison between calculated and measured amount of glass necessary for vitrification for different firing conditions and body compositions. The dashed lines represent the 99% confidence interval.
The average amount of glass phase measured over this experimentation range is 57.0 ±3.0% on a weight basis or 61.5 ±3.0% on a volume basis. This amount is higher than the values reported by Lerdprom8 (53.3 ±0.9% weight basis) and Foster37 (52.0 ±1.5%
weight basis). The difference, however, can be explained by the difference in the body chemistry. Figure 23 shows the correlation with the glass level necessary for densification with flux level for a dwell time of one hour and incorporates the reported glass levels of Foster and Lerdprom. The data from Foster fits perfectly with a flux content of 4.4%.
Lerdprom’s data, for a flux level of 3.0%, deviates from the trend, to a higher than predicted level, but is still within the margin of error. Lerdprom’s deviation may also be associated with his experimental conditions and his definition of the densification point.
41 R2O+RO
3 4 5 6 7 8
Amount of glass for densification (Weight%)
48 50 52 54 56 58 60 62 64 66
Figure 23. Experimental data for amount of glass necessary for densification for a dwell time of one hour. The blue dot represents the value reported by Foster37 and the red dot by Lerdprom.8
42
SUMMARY AND CONCLUSIONS
The results of this work verify previous work addressing the firing behavior of porcelain bodies and demonstrate that the firing behavior predictions are valid for a broad range of porcelain body formulations. From this work it is evident that the mineralogy (mullite level, quartz dissolution, and glass chemistry) can be accurately predicted by knowing the initial chemistry and the firing conditions. The amount of mullite that can be precipitated during firing is a straightforward calculation based on the difference between the overall Al2O3 in the body less the amount of Al2O3 that can be incorporated into the glass phase (1.16 (±0.06) moles of Al2O3 per mole of flux). Quartz dissolution and the glass chemistry scale linearly with temperature and with a log dwell time dependence.
This work also demonstrates that the densification temperature is determined by the flux content. This allows a more comprehensive opportunity to predict either the firing conditions necessary for densification (with a given body formulation) or the body composition necessary for specified firing schedule. This is an important contribution to the understanding of porcelains and to the ceramics field in general. From a practical perspective, the models generated in this thesis can be used to eliminate the need for extensive experimentation for industrial process revisions thus saving time and energy.
The density of the glass phase was calculated from the experimental data as 2.39 (±0.02) g/cm3. The amount of glass necessary for the vitrification of the porcelain body, at the proper densification temperature, can be calculated from the flux level and dwell time, with an average value of 57.0% (±3.0) on a weight basis or 61.5% (±3.0) on a volume basis.
The activation energy required to complete the maturing of the porcelain in the final stage of the densification process was calculated as 872 (±75) kJ/mol). It is not clear what this value represents, however, since there are several processes occurring simultaneously during the firing process. Regardless of the physical meaning of this value, these results are also consistent with some of the reported values in the literature. This activation energy value also appears to be independent of the overall chemistry of the body, and does not appear to change with changing flux level.
43
REFERENCES
1. C. M. Guinot and J. P. Saez, “Evolution of Porcelain Tile Decoration and Production Techniques,” Proceedings of the VII World Congress on Ceramic Tile Quality, Qualicer 2002, 15–18 (2002).
2. E. Sánchez, J. García-Ten, V. Sanz, and A. Moreno, “Porcelain Tile: Almost 30 Years of Steady Scientific-Technological Evolution,” Ceram. Int., 36 [3] 831–45 (2010).
3. D. U. Tulyaganov, H. R. Fernandes, S. Agathopoulos, and J. M. F. Ferreira,
“Influence of Lithium Oxide as Auxiliary Flux on the Properties of Triaxial Porcelain Podies,” J. Eur. Ceram. Soc., 26 [7] 1131–9 (2006).
4. M. D. Noirot, “Formulating Porcelain Bodies with Borax Auxiliary Flux,” Ceram.
Eng. Sci. Proc., 23 [2] 57-9 (2002).
5. A. Moreno, J. Garcia-Ten, E. Bou, and A. Gozalbo, “Using Boron as an Auxiliary Flux in Porcelain Tile Compositions,” Proceedings of the IV World Congress on Ceramic Tile Quality, Qualicer 2000, 77–91 (2000).
6. L. Esposito, A. Salem, A. Tucci, A. Gualtieri, and S. H. Jazayeri, “The Use of Nepheline-Syenite in a Body Mix for Porcelain Stoneware Tiles,” Ceram. Int., 31 [2]
233–40 (2005).
7. A. Salem, S. H. Jazayeri, E. Rastelli, and G. Timellini, “Dilatometeric Study of Shrinkage During Sintering Process for Porcelain Stoneware Body in Presence of Nepheline Syenite,” J. Mater. Process. Technol., 209 [3] 1240–6 (2009).
8. W. Lerdprom, “Firing of Porcelain,” M.S. Thesis, Alfred University, Alfred, NY, 2014.
9. F. H. Norton, Fine Ceramics: Technology and Applications, pp. 258-80. Robert E.
Krieger Publishing Company, Inc., Malabar, FL, 1978.
44
10. M. N. Rahaman, Ceramic Processing, 2nd Ed., pp 412-21. CRC Press, Boca Raton, FL, 2007.
11. W. M. Carty and U. Senapati, “Porcelain-Raw Materials, Processing, Phase Evolution and Mechanical Behavior,” J. Am. Ceram. Soc., 81 [1] 3–20 (1998).
12. N. G. Holmström, “Fast firing of Triaxial Porcelain,” Am. Ceram. Soc. Bull., 60 [4]
470–3 (1981).
13. E. Skovira, “Properties of the Porcelain Glass Phase,” M.S. Thesis, Alfred Univerity, Alfred, NY, 2006.
14. Y. Iqbal and W. E. Lee, “Fired Porcelain Microstructures Revisited,” J. Am. Ceram.
Soc., 82 [12] 3584–90 (1999).
15. Y. Iqbal and W. E. Lee, “Microstructural Evolution in Triaxial Porcelain,” J. Am.
Ceram. Soc., 83 [12] 3121–27 (2000).
16. W. E. Lee, G. P. Souza, C. J. McConville, T. Tarvornpanich, and Y. Iqbal, “Mullite Formation in Clays and Clay-Derived Vitreous Ceramics,” J. Eur. Ceram. Soc., 28 [2] 465–71 (2008).
17. W. E. Lee and Y. Iqbal, “Influence of Mixing on Mullite Formation in Porcelain,” J.
Eur. Ceram. Soc., 21 [14] 2583–6 (2001).
18. W. M. Carty, “Observations on the Glass Phase Composition in Porcelains,” Ceram.
Eng. Sci. Proc., 23 [2] 79–94 (2002).
19. D. I. Seymour, “Phase evolution in electrical porcelains during firing,” M.S. Thesis, Alfred University, Alfred, NY, 2000.
20. H. Mörtel, "Influencing of the Processing Parameters on the Properties of Rapid Fired Porcelain"; pp. 253-62 in Materials Science Research, Vol. 11, Processing of Crystalline Ceramics. Edited by. H. Palmour III, R. F. Davis and T. M. Hare.
Springer, New York, 1978.
45
21. B. Pinto, “Effect of Filler Particle Size on Porcelain Strength,” M.S. Thesis, Alfred Univerity, Alfred, NY, 2001.
22. G. Stathis, A. Ekonomakou, C. J. Stournaras, and C. Ftikos, “Effect of Firing Conditions, Filler Grain Gize and Quartz Content on Bending Strength and Physical Properties of Sanitaryware Porcelain,” J. Eur. Ceram. Soc., 24 [8] 2357–66 (2004).
23. F. H. Norton and F. B. Hodgdon, “The Influence of Time on the Maturing Temperature of Whiteware Bodies. I,” J. Am. Ceram. Soc., 14, 177–91 (1931).
24. W. W. Meyer, “Computation of Heat Treatments for Whiteware Bodies,” J. Am.
Ceram. Soc., 21, 75–9 (1938).
25. S. Y. Reyes, J. Serrato, and S. Sugita, “Determination of the Activation Energy for Densification of Porcelain Stoneware,” J. Ceram. Process. Res., 12 [3] 228–32 (2011).
26. C. Dannert, B. Durschang, F. Raether, and F. Becker, “Optimization of Sintering Processes for Porcelain Using In-Situ Measuring Methods,” Materials Week 2000, Munich Germany, Symposium I3 Process Development, 1–6 (2000).
27. M. Romero, J. Martin-Márquez, and J. M. Rincón, “Kinetic of Mullite Formation from a Porcelain Stoneware Body for Tiles Production,” J. Eur. Ceram. Soc., 26 [9]
1647–52 (2006).
28. C. Zanelli, M. Raimondo, M. Dondi, G. Guarini, and P. M. Tenorio Cavalcante,
“Sintering Mechanisms of Porcelain Stoneware Tiles,” Proceedings of the VIII World Congress on Ceramic Tile Quality, Qualicer 2004, 1, 247–259 (2004).
29. Ferro GmbH Performance Pigments and Colors, Process Temperature Control Rings (PTCR). Gutleuststr, Germany, 2012.
30. “Standard Test Method for Water Absorption, Bulk Density, Apparent Porosity, and Apparent Specific Gravity of Fired Whiteware Products, Ceramic Tiles, and Glass
46
Tiles,” ASTM Designation C 373-14. American Society for Testing and Materials, West Conshohocken, PA.
31. H. Lee and W. M. Carty, "Glass Phase Composition in Porcelains and Correlation with Firing Temperature", in Proceedings of the 106th Annual Meeting and Exposition of the American Ceramic Society, April 18–21 2004, Indianapolis, IN, 2004.
32. A. Shah, “The Glass Formation Boundary in Porcelains”; M.S. Thesis. Alfred University, Alfred, NY, 2007.
33. S. T. Lundin, “Microstructure of porcelain,” Natl. Bur. Stand. Misc. Publ., 257, 93–
106 (1964).
34. S. T. Lundin, Studies on Triaxial Whiteware Bodies, pp 87-9. Almqvist and Wiksell, Stockholm, 1959.
35. M. M. Smedskjaer, J. C. Mauro, J. Kjeldsen, and Y. Yue, “Microscopic Origins of Compositional Trends in Aluminosilicate Glass Properties,” J. Am. Ceram. Soc., 96 [5] 1436–43 (2013).
36. J. E. Shelby, Introduction to Glass Science and Technology, 2nd ed.; pp. 72-110. TJ International Limited, Padstow, UK, 2005.
37. A. Foster, “Dependence of Porcelain Densification on Body Glass Content,” B.S.
Thesis, Alfred University, Alfred, NY, 2013.
47
APPENDIX
48 A. Quantitative x-ray diffraction data
Table VIII. Quantitative X-ray Diffraction Data for Vitrified Samples Body
batch R2O+RO
(%mol) Temp.
(°C) Dwell
time (hr)
Mullite (%WB
)
Quartz
(%WB) Glass
(%WB) Glass
density (g/cm3)
Al2O3 in glass (UMF)
1 5.27 1285 0.32 21.28 23.43 55.27 2.39 1.24
2 4.84 1290 0.32 24.96 21.60 53.42 2.38 1.11
3 6.35 1255 0.32 24.24 17.93 57.81 2.40 1.11
4 5.92 1270 0.32 22.85 20.97 56.16 2.39 1.13
5 6.01 1260 0.32 21.85 22.47 55.66 2.38 1.04
6 6.67 1245 0.32 22.05 20.65 57.29 2.41 1.09
7 4.84 1295 0.32 20.81 26.28 52.88 2.39 1.21
8 5.58 1275 0.32 25.18 18.55 56.26 2.38 1.15
9 5.80 1270 0.32 22.03 20.20 57.74 2.40 1.20
10 5.23 1285 0.32 27.75 17.04 55.19 2.37 1.14
11 5.76 1270 0.32 21.55 20.04 58.39 2.40 1.27
12 7.34 1225 0.32 19.15 19.52 61.32 2.44 1.21
5 6.01 1285 0.10 20.07 24.85 55.06 2.40 1.19
5 6.01 1235 1.00 20.68 22.23 57.08 2.38 1.14
7 4.84 1320 0.10 21.87 27.31 50.80 2.35 1.11
7 4.84 1265 1.00 21.38 25.01 53.59 2.36 1.15
12 7.34 1250 0.10 19.55 20.30 60.12 2.41 1.18
12 7.34 1200 1.00 19.99 18.28 61.71 2.44 1.15
12 7.34 1200 1.00 19.32 17.56 63.10 2.38 1.20
12 4.84 1295 0.32 20.75 25.92 53.30 2.39 1.22
6 6.67 1270 0.10 21.11 21.73 57.14 2.41 1.16
6 6.67 1220 1.00 20.85 18.56 60.58 2.40 1.18
12 7.34 1225 0.32 20.36 18.33 61.30 2.39 1.13
3 6.35 1280 0.10 25.05 19.30 55.63 2.38 1.05
3 6.35 1230 1.00 23.44 16.89 59.65 2.42 1.17
49
B. Correlation matrix for the amount of mullite with the firing parameters and initial composition of the porcelain body
Al2O3 in glass UMF
Kaolinite (%WB) -0.162 0.439
Fe2O3 (%WB) 0.003 0.990 R2O+RO (%mol) -0.051 0.809 Temperature (°C) -0.046 0.826 Dwell time (hour) 0.127 0.544
Cell content: Pearson coefficient P-Value
With a confidence level of 95%, is possible to conclude that there is no correlation between the amount of Al2O3 in the glass phase with composition of the porcelain body and the firing parameters (The P-Values for all parameters are greater than 0.05).
C. Correlation analysis for the model to predict the amount of undissolved quartz in the final body
50 The regression equation is:
Und. Quartz(Qinitial/Qfinal) = 3.91-0.00251*T(°C)- 0.237*Log[t(hr)]
Predictor Coef Coef. of EE T P Constant 3.9108 0.1948 20.08 0.000 Temperature (°C) -0.0025123 0.0001579 -15.91 0.000 Log (Dwell time-hr) -0.23740 0.01447 -16.40 0.000
S = 0.0186564 R-sqr. = 93.6% R-sqr.(ajusted) = 93.0%
ANOVA Table
Source DF SC MC F P-value Regression 2 0.111773 0.055887 160.57 0.000 Residual Error 22 0.007657 0.000348
Total 24 0.119431
The p-values of the coefficients and the regression are lower than 0.05, which confirms the statistical significance of the regression model.
93% of the observed variation in the amount of undissolved quartz can be explained through the empirical model (R-sqr adjusted=93.0%).
Figures 24 and 25 show the residual analysis for the model. There are no patterns in the residual plots, so that the samples are random and independent (the assumption of equal variance for the different treatments is fulfilled). The residuals are not normally distributed according to Figure 24, although, the equal variances assumption was confirmed and the analysis of variances can assumed to be enough to validate the model.
51
Figure 24. Residual analysis for Undissolved Quartz in the initial porcelain body.
Figure 25. Normal probability plot for residues (Undissolved Quartz model).
0.050 0.025
0.000 -0.025
-0.050 99 90 50 10 1
Residue
Porcentage
1.0 0.9
0.8 0.7
0.02
0.00 -0.02 -0.04
Adjusted value
Residuo
0.02 0.01 0.00 -0.01 -0.02 -0.03 -0.04 8 6 4 2 0
Residue
Frecuency
24 22 20 18 16 14 12 10 8 6 4 2 0.02
0.00
-0.02
-0.04
Run sequence
Residue
Normal probability plot vs. ajusted values
Histogram vs. run sequence
Residual plots for Undisolv Quartz (initial/final)
0.050 0.025
0.000 -0.025
-0.050
99
95 90 80 70 60 50 40 30 20 10 5
1
Residue
Porcentage
Mean -1.77636E-15 Std. Dev. 0.01786
N 25
AD 0.831
P-Value 0.027
Normal probability plot for Residuals (Undisolved Quartz model) Normal - 95% CI
52
D. Correlation analysis for the model to predict SiO2 in the glass phase The regression equation is:
SiO2 in glass UMF = - 42.2 + 0.0404 Temperature (°C) + 2.57 Log (Dwell time-hr)
Predictor Coef Coef. of EE T P Constant -42.178 2.272 -18.57 0.000 Temperature (°C) 0.040435 0.001842 21.95 0.000 Log (Dwell time-hr) 2.5740 0.1688 15.25 0.000
S = 0.21761 R-sqr. = 95.7% R-sqr.(ajusted) = 95.3%
ANOVA Table
Source DF SC MC F P-value Regression 2 22.985 11.492 242.69 0.000 Residual Error 22 1.042 0.047
Total 24 24.027
The p-values of the coefficients and the regression are lower than 0.05, which confirms the statistical significance of the regression model.
95.3% of the observed variation in the SiO2 level of the glass phase can be explained through the empirical model (R-sqr adjusted=95.3%).
Figures 26 and 27 show the residual analysis for the model. There are no patterns in the residual plots, so that the samples are random and independent (the assumption of equal variance for the different treatments is fulfilled). The residuals are normally distributed and therefore the assumption of normal distribution is fulfilled, the observations come from normally distributed populations.
53
Figure 26. Residues plot for SiO2 in the glass phase model
Figure 27. Normal probability plot for residues (SiO2 in glass phase model)
0.50 0.25
0.00 -0.25
-0.50 99 90 50 10 1
Residue
Porcentage
9 8
7 6
0.50 0.25 0.00 -0.25 -0.50
Adjusted value
Residue
0.4 0.2 0.0 -0.2 -0.4 8 6 4 2 0
Residue
Frecuency
24 22 20 18 16 14 12 10 8 6 4 2 0.50 0.25 0.00 -0.25 -0.50
Run secuence
Residuo
Normal probability plot vs. Ajusted values
Histogram vs. Run secuence
Residues plot for SiO2 in glass phase (UMF)
0.75 0.50
0.25 0.00
-0.25 -0.50
99
95 90 80 70 60 50 40 30 20 10 5
1
Residue
Porcentage
Mean 2.486900E-16 Std. dev. 0.2083
N 25
AD 0.360
P-value 0.420
Normal - 95% de IC
Normal probability plot for Residues
54
E. Correlation analysis for the model to predict glass amount necessary for vitrification
The regression equation is:
Glass (%WB) = 39.5 + 3.13 R2O+RO (%mol) + 2.90 Log (Dwell time-hr)
Predictor Coef Coef. of EE T P Constant 39.494 1.402 28.18 0.000 R2O+RO (%mol) 3.1269 0.2205 14.18 0.000 Log (Dwell time-hr) 2.9003 0.5765 5.03 0.000 S = 0.95045 R-sqr. = 91.6% R-sqr.(ajusted) = 90.9%
ANOVA Table
Source DF SC MC F P-value Regression 2 217.74 108.87 120.51 0.000 Residual Error 22 19.87 0.90
Total 24 237.61
The p-values of the coefficients and the regression are lower than 0.05, which confirms the statistical significance of the regression model.
90.9% of the observed variation in the SiO2 level of the glass phase can be explained through the empirical model (R-sqr adjusted=90.9%).
Figures 28 and 29 show the residual analysis for the model. There are no patterns in the residual plots, so that the samples are random and independent (the assumption of equal variance for the different treatments is fulfilled). The residuals are normally distributed and therefore the assumption of normal distribution is fulfilled, the observations come from normally distributed populations.
55
Figure 28. Residues plot for amount of glass necessary for vitrification model.
Figure 29. Normal probability plot for residues (Amount of glass necessary for vitrification model).
2 1
0 -1 -2
99 90 50 10 1
Residuo
Porcentage
63 60
57 54
51 2 1 0 -1 -2
Adjusted value
Residuo
2 1
0 -1
6.0 4.5 3.0 1.5 0.0
Residue
Frecuency
24 22 20 18 16 14 12 10 8 6 4 2 2 1 0 -1 -2
Run secuence
Residue
Normal probability plot vs. Adjusted values
Histogram vs. Run secuence
Gráficas de residuos para Glass (%WB)
3 2
1 0
-1 -2
-3
99
95 90 80 70 60 50 40 30 20 10 5
1
Residuals
Porcentage
Mean -1.79057E-14 Std. dev. 0.9100
N 25
AD 0.273
P-Value 0.638
Gráfica de probabilidad de RESID Glass Normal - 95% CI
56
F. Correlation analysis for the model to predict vitrification temperature The regression equation is:
Vit Temp (°C) = 1398 - 26.9 R2O+RO (%mol) - 51.1 Log(Dwell tim_hr
Predictor Coef Coef. of EE T P Constant 1398.27 4.59 304.87 0.000 R2O+RO (%mol) -26.9187 0.7735 -34.80 0.000 Log(Dwell tim_hr) -51.097 1.545 -33.07 0.000
S = 4.23210 R-sqr. = 97.6% R-sqr.(ajusted) = 97.5%
ANOVA Table
Source GL SC MC F P Regression 2 41273 20636 1152.18 0.000 Residual error 57 1021 18
Total 59 42294
The p-values of the coefficients and the regression are lower than 0.05, which confirms the statistical significance of the regression model.
97.5% of the observed variation in the SiO2 level of the glass phase can be explained through the empirical model (R-sqr adjusted=97.5%).
Figures 30 and 31 show the residual analysis for the model. There are no patterns in the residual plots, so that the samples are random and independent (the assumption of equal variance for the different treatments is fulfilled). The residuals are normally distributed and therefore the assumption of normal distribution is fulfilled, the observations come from normally distributed populations.
57
Figure 30. Residues plot for vitrification temperature model.
Figure 31. Normal probability plot for residues (Vitrification temperature model).
10 5 0 -5 -10 99.9
99 90 50 10 1 0.1
Residue
Porcentage
1320 1290
1260 1230
1200 10
5 0 -5 -10
Adjusted value
Residue
10 5
0 -5 -10 20
15 10 5 0
Residue
Frecuency
60 55 50 45 40 35 30 25 20 15 10 5 1 10
5 0 -5 -10
Run secuence
Residuo
Normal probability plot vs. Adjusted values
Histogram vs. Run secuence
Gráficas de residuos para Vit Temp (°C)
20 10
0 -10
-20
99.9
99 95 90 80 7060 5040 30 20 10 5 1 0.1
Reisdue
Porcentage
Mean 4.812743E-13 Std. Dev. 4.160
N 60
AD 0.437
P-Value 0.287
Gráfica de probabilidad de RESID1 Normal - 95% CI
58
G. Hypothesis test for water absorption of 0.2%
A one sample Z-test, which is a hypothesis test for sample size bigger than 30, was done to verify the statistical significance of the water absorption data; it was found that the hypothetical water absorption value of 0.20% is located within the confidence interval of the sample mean (0.18% to 0.22%), thus there is no statistical significance in the difference between the experimental and the hypothetical value predicted by the model:
Test for mu = 0.2 vs. no = 0.2 Assumed standard deviation = 0.11264
Mean of the Standard
Variable N Mean Std. Dev. Error 95% Conf. Int. Z P Abs 144 0.20204 0.11264 0.00939 (0.18364, 0.22044) 0.22 0.828
The histogram for the data along with the confidence interval of the sample mean and the hypothetical mean is shown in Figure. 32.