400 B.C. 131 138 125 129 132 135 132 134 138 1850 B.C. 129 134 136 137 137 129 1136 138 134 150B A.C. 128 138 136 139 141 142 137 145 137 Listed on the top are skull breadths obtained from skulls of Egyptian makes from three different epochs( based on the data from Ancient Races of the Thebaid by Thomson and Randall-Maciver). Assume that we plan to use analysis of variance with a 0.05 significance level to test the claim that the different epochs have mean skull breadths that are not all the same. The results from XI.STAT are shown down below. Source DF Sum of squares Means squares F Pr>F Model 2 138.7407 69.3704 4.0497 0.0305 Error 24 411.1111 17.1296 Corrected Total 26 549.8519 1- ANOVA What characteristic of the data indicates that we should use one-way analysis of variance? 2- Null and Alternative Hypotheses For the hypothesis test described in Exercise 1, identify the null hypothesis and the alternative hypothesis. 3- Test statistic Identify the value of the test statistic in the display included with Exercise 1. In general, do larger test statistic result in larger P-values, smaller P-values that are unrelated to the value of the test statistic? 4- Conclusions If the best described in Exercise 1 is conducted with a 0.05 significance level, what should be concluded about the null hypothesis? What do the results suggest about the data? 5-Type of test Is the hypothesis test described in Exercise 1 left-tailed, right-tailed or two-tailed? Are all one-way analysis of variance tests left-tailed, right-tailed, or two-tailed? 6- Which Mean is different? For the three samples described in Exercise 1, if we use analysis of variance and reach a conclusion to reject equality of the three population means, can we then conclude that any of the specific population has a mean that is different from the others? 7-One vs Two What is the fundamental difference between one-way analysis of variance and two-way analysis of variance?
| 400 B.C. | 131 | 138 | 125 | 129 | 132 | 135 | 132 | 134 | 138 |
| 1850 B.C. | 129 | 134 | 136 | 137 | 137 | 129 | 1136 | 138 | 134 |
| 150B A.C. | 128 | 138 | 136 | 139 | 141 | 142 | 137 | 145 | 137 |
Listed on the top are skull breadths obtained from skulls of Egyptian makes from three different epochs( based on the data from Ancient Races of the Thebaid by Thomson and Randall-Maciver). Assume that we plan to use analysis of variance with a 0.05 significance level to test the claim that the different epochs have mean skull breadths that are not all the same. The results from XI.STAT are shown down below.
| Source | DF | Sum of squares | Means squares | F | Pr>F |
| Model | 2 | 138.7407 | 69.3704 | 4.0497 | 0.0305 |
| Error | 24 | 411.1111 | 17.1296 | ||
| Corrected Total | 26 | 549.8519 |
1- ANOVA What characteristic of the data indicates that we should use one-way analysis of variance?
2- Null and Alternative Hypotheses For the hypothesis test described in Exercise 1, identify the null hypothesis and the alternative hypothesis.
3- Test statistic Identify the value of the test statistic in the display included with Exercise 1. In general, do larger test statistic result in larger P-values, smaller P-values that are unrelated to the value of the test statistic?
4- Conclusions If the best described in Exercise 1 is conducted with a 0.05 significance level, what should be concluded about the null hypothesis? What do the results suggest about the data?
5-Type of test Is the hypothesis test described in Exercise 1 left-tailed, right-tailed or two-tailed? Are all one-way analysis of variance tests left-tailed, right-tailed, or two-tailed?
6- Which Mean is different? For the three samples described in Exercise 1, if we use analysis of variance and reach a conclusion to reject equality of the three population means, can we then conclude that any of the specific population has a mean that is different from the others?
7-One vs Two What is the fundamental difference between one-way analysis of variance and two-way analysis of variance?
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