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To assess the reliability of timber structures and related building design codes, many researchers have studied strength factors of structural lumber. In one such study, three species of Canadian softwood were analyzed for bending strength. Varying numbers of observations were made for each species. Assume all three populations are normally distributed with equal variances. The results are given here: Bending Strength (in MPa) Mean (in MPa)

To assess the reliability of timber structures and related building design codes, many researchers have studied strength factors of structural lumber. In one such study, three species of Canadian softwood were analyzed for bending strength. Varying numbers of observations were made for each species. Assume all three populations are normally distributed with equal variances. The results are given here: Bending Strength (in MPa) Mean (in MPa)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Douglas-Fir Hem-Fir Spruce pine-Fir 75 45 42 57 48 39 51 33 30 33 Anova: Single Factor SUMMARY Groups Count Sum Average Variance Douglas-Fir 3 183 61 156 Hem-Fir 3 126 42 63 Spruce pine-Fir 4 144 36 30 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 1118.1 2 559.05 7.411648 0.018691 4.737414 Within Groups 528 7 75.42857 Total 1646.1 9
Transcribed Image Text:Douglas-Fir Hem-Fir Spruce pine-Fir 75 45 42 57 48 39 51 33 30 33 Anova: Single Factor SUMMARY Groups Count Sum Average Variance Douglas-Fir 3 183 61 156 Hem-Fir 3 126 42 63 Spruce pine-Fir 4 144 36 30 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 1118.1 2 559.05 7.411648 0.018691 4.737414 Within Groups 528 7 75.42857 Total 1646.1 9
To assess the reliability of timber structures and related building design codes, many researchers have studied strength factors of structural lumber. In one such study, three species of Canadian softwood were analyzed for bending strength. Varying numbers of observations were made for each species. Assume all three populations are normally distributed with equal variances. The results are given here: Bending Strength (in MPa) Mean (in MPa) Douglas-Fir 75, 57, 51 61 Hem-Fir 45, 48, 33 42 Species Spruce Pine- 42, 39, 30, 33 Fir a) State the null and alternative hypotheses. Null Ho: Hi = Hz = M3 Alternative Ha Not all the population means are equal b) Construct the appropriate ANOVA table. Anova: Single Factor SUMMARY Douglas-Fir Hem-Fir Spruce pine-Fir Groups Count Sum Average Variance 75 45 42 57 48 39 Douglas-Fir 3 183 61 156 51 33 30 Hem-Fir 126 42 63 33 Spruce pine-Fir 144 36 30 ANOVA Source of Variation SS df MS P-value E crit Test statistic value : 7.4|16 Between Groups 1118.1 2 559.05 7.411648 0.018691 4.737414 Within Groups 528 7 75.42857 P-value is : 0.0187 Total 1646.1 9 c) Use the ANOVA table from part b) to test whether there is a difference in the mean bending strengths among the three types of wood at the .05 level. Given that the level of significance is 0.05. Here , the p-value (0.0187) is less than the level of significance (0.05). Therefore, reject the null hypothesis. Thus, there is difference in mean bending strengths among the 3 types of wood. d) Is it applicable to follow up with Tukey-Kramer pairwise comparisons? Why or why not? e) Determine which pair(s) of means are significantly different using the Tukey-Kramer method. 37
Transcribed Image Text:To assess the reliability of timber structures and related building design codes, many researchers have studied strength factors of structural lumber. In one such study, three species of Canadian softwood were analyzed for bending strength. Varying numbers of observations were made for each species. Assume all three populations are normally distributed with equal variances. The results are given here: Bending Strength (in MPa) Mean (in MPa) Douglas-Fir 75, 57, 51 61 Hem-Fir 45, 48, 33 42 Species Spruce Pine- 42, 39, 30, 33 Fir a) State the null and alternative hypotheses. Null Ho: Hi = Hz = M3 Alternative Ha Not all the population means are equal b) Construct the appropriate ANOVA table. Anova: Single Factor SUMMARY Douglas-Fir Hem-Fir Spruce pine-Fir Groups Count Sum Average Variance 75 45 42 57 48 39 Douglas-Fir 3 183 61 156 51 33 30 Hem-Fir 126 42 63 33 Spruce pine-Fir 144 36 30 ANOVA Source of Variation SS df MS P-value E crit Test statistic value : 7.4|16 Between Groups 1118.1 2 559.05 7.411648 0.018691 4.737414 Within Groups 528 7 75.42857 P-value is : 0.0187 Total 1646.1 9 c) Use the ANOVA table from part b) to test whether there is a difference in the mean bending strengths among the three types of wood at the .05 level. Given that the level of significance is 0.05. Here , the p-value (0.0187) is less than the level of significance (0.05). Therefore, reject the null hypothesis. Thus, there is difference in mean bending strengths among the 3 types of wood. d) Is it applicable to follow up with Tukey-Kramer pairwise comparisons? Why or why not? e) Determine which pair(s) of means are significantly different using the Tukey-Kramer method. 37
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