Consider the dataset from Exercises 15.1 and 17.6 consisting of measured chest circumferences of Scottish soldiers with average ¯xn = 39.85 and sample standard deviation sn = 2.09. The histogram in...

Consider the dataset from Exercises 15.1 and 17.6 consisting of measured chest circumferences of Scottish soldiers with average ¯xn = 39.85 and sample standard deviation sn = 2.09. The histogram in Figure 17.11 suggests modeling the data as the realization of a random sample X1, X2,...,Xn from an N(µ, σ2) distribution. We estimate µ by the sample mean and we are interested in the probability that the sample mean deviates more than 1 from µ: P  |
_n
− µ| > 1  . Describe how one can use the bootstrap principle to approximate this probability, i.e., describe the distribution of the bootstrap random sample X∗

₁
, X^∗

2 ,...,X^∗

_n
and compute P| ∗ n − µ∗| > 1  . Note that one does not need a simulation to approximate this latter probability