To appreciate the importance of setting the location functional, consider the length of rivers data set, as taken from Tukey (1977)

To appreciate the importance of setting the location functional, consider the length of rivers data set, as taken from Tukey (1977). This data set contains the lengths of 141 American rivers in miles and it can be found in the file lengthriver.rda.

(a) Suppose the location functional is the median. Obtain the estimate and a 95% confidence interval for it. Use the confidence interval discussed in Section 10.2.3. Interpret it in terms of the data. Use the R function onesampsgn.R for computation.

(b) Suppose the location functional is the mean. Obtain the estimate and the 95% t-confidence interval for it. Interpret it in terms of the data.

(c) Obtain the boxplot of the data and sketch the estimates and confidence intervals on it. Discuss.