Further Reading
Statistics for Experimenters by Box, Hunter and Hunter [3] introduces a large number of useful hypothesis tests using practical examples and is highly recommended as a reference book for experimenters. It also treats statistical modeling. Two other books that provide good introductions to statistical modeling are Statistics: an introduction using R by Crawley [4] and Multivariate data analysis by Hair, Anderson, Tatham, and Black [5].
ANSWERS FOR EXERCISES
8.1 A mean fuel consumption of 5.84 liters per 100 km is needed to provide a significant result at the 95% confidence level.
8.2 Reading from the table of probability points for the t-distribution in the Appendix, t0.05,4= 2.132. The one-sided confidence interval lies below 6.14.
8.3 tobs = 2.064. The t-table in the Appendix gives tcrit= t0.05,5 = −2.015. As tobs >> tcrit the null hypothesis is strongly supported. (Note thattcrit is negative due to the “≥” in the null hypothesis, which means that it will be discredited by observations in the left tail of the distribution, and that forgetting the minus sign would reverse the conclusion.)
8.3 The mean difference is 0.08. Using the pooled standard deviation this yields a tobs of 0.8. The critical t-values for this two sided test are t0.025,8= ±2.306. Since tobs is within these boundaries H0 is supported: the data suggest that there is no significant difference between the summer and winter fuel consumption.
8.4 The ANOVA table should look like the following. There is a difference between the treatments that is significant at the 95% confidence level.
8.5 The ANOVA table should look like:
References
1. Fisher, R.A. (1951) The Design of Experiments, 6th edn, Oliver and Boyd, Edinburgh.
2. Huitson, A. (1966) The Analysis of Variance, Charles Griffin & Co., London.
3. Box, G.E.P., Hunter, J.S., and Hunter, W.G. (2005) Statistics for Experimenters: Design, Innovation, and Discovery, 2nd edn, John Wiley & Sons, Inc., Hoboken (NJ).
4. Crawley, M.J. (2005) Statistics: An Introduction Using R, John Wiley & Sons Ltd, Chichester.
5. Hair, J.F., Anderson, R.E., Tatham, R.L., and Black, W.C. (1998) Multivariate Data Analysis, 5th edn, Prentice-Hall, Upper Saddle River (NJ).
