22, 36, 44*, 60, 69, 72.
*You can adapt the R function
samplemeans()from the Feb. 4 lecture. Assess normality with histograms and normal probability plots. Repeat the exercise to get the sampling distribution of the sample median. Which statistic has the smaller standard error, the sample mean or the sample median? Use R to reproduce Fig. 5.6.
4, 12, 22*
*Note that you can express the moment estimate in terms of the sample mean and the MLE in terms of the geometric mean. (The geometric mean is the nth root of the product of all the observations.) Draw a histogram of the data and superimpose a plot of the density function fitted with the MLE of q. This distribution is a special case of one of the distributions introduced in Chapter 4. Which one?
8, 10, 40, 44, 56