# Bootstrap Confidence Intervals for the difference of means

hello,
I'm trying to calculate the coverage probability for Bootstrap Confidence Intervals for the difference in means , but I always get unreasonable results.
I want to create two examples where the data is simulated and one of the examples i want to have a Coverage probability around 0.95 and in the other example i want the Coverage probability to be different from 0.95 (far). for that i did 2 thing : for the first example i sampled data from exponential(rate=3) and for the second example i sampled data from normal(mu=4,sd=7) and exponential(rate=1).
for calculating one bootstrap CI i created a function that takes the "simulated data" (X and Y) and its difference of means (denoted as T_stat) as arguments and returns 1 if the CI includes the T_stat otherwise it returns 0.
then to compute the CP, i used replicate to create B=1000 CI indicators and took the mean of them.
i beileve the problem is in the function which i called "boot_fun" but i cant figure what it is.

the photo attached id for the code of example 2 i tried to create (samples from different distributions) but for example 1 (with the same distribution) i used the code the difference only where i sample X and Y for the first time. ``````set.seed(4)
n <- 200
m <- 300
B <- 1000

X <- rnorm(n, mean = 4, sd = 7)
Y <- rexp(n, rate = 1)

X_bar <- mean(X)
Y_bar <- mean(Y)
T_stat <- X_bar-Y_bar

#Bootstrap

Boot_func <- function(X,Y){
n <- length(X)
m <- length(Y)
joint <- c(X,Y)
X_star <- sample(joint, n, replace=T)
Y_star <- sample(joint, m, replace=T)
X_star_bar <- mean(X_star)
Y_star_bar <- mean(Y_star)
Diff <- X_star - Y_star
CI <- quantile(Diff, c(0.025,0.975))
Indicate <- between(T_stat,CI,CI)
return(Indicate)
}

CP2 <- mean(replicate(B, Boot_func(X,Y)))

``````

Hi, can you post your actual code, rather than a screenshot of it?

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