Further Reading
The contents of this chapter are described in most elementary textbooks on statistics. Many such books take a rather mathematical approach to the subject. It is often beneficial for the understanding to present statistical ideas and tools by practical examples. Statistics for Experimenters by Box, Hunter and Hunter [1] does so in a clear way and is probably one of the better statistics books available for people doing experimental work. Those readers who want to write programs for statistical analysis might consider Statistics – an introduction using R by Crawley [2]. “R” is a freely available language and environment for statistical computing and graphics. It is platform independent and can be downloaded at http://cran.r-project.org/.
ANSWERS FOR EXERCISES
7.1 Make a numbered list over all addresses in the nation. Draw the numbers using a random number generator, for example using the Excel function = RAND().
7.2 Mean = 7.22, median = 7, mode = 7.
7.3 Mean = 3, median = 3 for all three dot plots. The range is 0 in the top dot plot and 4 in the other two.
7.4 Standard deviation = 3.96.
7.5 See the answer for Exercise 8.9 and the discussion of these data in connection to the one-sample t-test in Chapter 8.
7.6 See the discussion of these data in connection to the two-sample t-test in Chapter 8.
7.7 Z= 1.61. The cumulative probability F(Z) = 0.9463 (read from the table of standard normal probabilities in the Appendix). The probability of finding a rate greater or equal to that in Caramel is 1 − F(Z) = 0.0537. A more exact value can be calculated in Excel using the expression = 1-NORMSDIST(Z).
7.8 According to the central limit theorem, the means of samples tend to be normally distributed for large sample sizes. The caries rate in a town is the mean of a sample consisting of all its inhabitants. Since the central limit theorem applies, it is reasonable to expect a normal distribution.
7.9 Reading from the table over probability points for the t-distribution in the Appendix, t0.025, 4= 2.776. The confidence interval lies between 5.8 and 6.2 liters per 100 km.
References
1. 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).
2. Crawley, M.J. (2005) Statistics: An Introduction Using R, John Wiley & Sons Ltd, Chichester.
Strictly speaking, this experiment would need a control group to ensure that the effect is due to the diet and not to a background factor. For further discussion, see the section “Reflections on the exhibition” in Chapter 6 and “Designs with one categorical factor” in Chapter 9.
