A quality control engineer collects a sample of gears, examining 20 gears from the manufacturing line. She is interested in estimating the mass of the gears, with a 93 % confidence interval. However, she is not confident in the normality of the observed data, and would like to estimate the Standard Error using the bootstrap. To do this, take the data below, and using the boot function from the boot package, with set.seed(93) for randomization, and R = 1e4 replicates, estimate the SE of the mean. Then, using this SE and the appropriate t quantile (20 - 1 df), find the 93 % confidence interval.'

dat <- c(15.24, 14.26, 19.7, 15.56, 26.16, 14.92, 13.95, 19.48, 20.28, 20.74, 22.88, 20.3, 21.65, 16.06, 18.35, 23.08, 20.41, 23.76, 14.31, 19.05)

The Standard Error for X-bar =

The 93 % Confidence Interval for X-bar (Lower, then Upper) __________, ____________