Consider Part (a) of Exercise 6.4.6.
(a) Using the data of Exercise 6.4.7, compute the mle of b. Also obtain the estimate based on 90th percentile of the data.
(b) Edit the R function bootstrapcis64.R to compute a bootstrap confidence interval for b. Then run your R function on the data of Exercise 6.4.7 to compute a 95% confidence interval for b.
Exercise 6.4.7
The data file normal50.rda contains a random sample of size n = 50 for the situation described in Exercise 6.4.6. Download this data in R and obtain a histogram of the observations.
Exercise 6.4.6
Let 
be a random sample from 
(a) If the constant b is defined by the equation 
find the mle of b.
(b) If c is given constant, find the mle of
(a) In Part (b) of Exercise 6.4.6, let c = 58 and let ξ = P(X ≤ c). Based on the data, compute the estimated value of the mle for ξ. Compare this estimate with the sample proportion, ˆp, of the data less than or equal to 58.
(b) The R function bootstrapcis64.R computes a bootstrap confidence interval for the mle. Use this function to compute a 95% confidence interval for ξ. Compare your interval with that of expression (4.2.7) based on ˆp.