Constructing confidence intervals for trimmed means in R - r

Question

I'd like to test the coverage probabilities for trimmed means, I am using the formula form Wilcox book for confidence intervals:
Confidence interval
The s_w is Winsorised variance and γ is the proportion coefficient, in my code it's denoted as alpha. The problem is, that the code, I have made outputs confidence intervals with 0 always in them, so that the coverage probability is 1. So, I think there is some error in the construction.
Code:
sample_var <- function(data, alpha){
n <- length(data)
data <- sort(data)
data_t <- data[(floor(n*alpha)+1):(n-floor(alpha*n))]
m <- length(data_t)
t_mean <- mean(data_t)
sigma <- (1/(1-2*alpha)^2)* ((1/n) *sum((data_t-t_mean)^2)+ alpha*(data_t[1]-t_mean)^2 +
alpha*(data_t[m]-t_mean)^2)
sigma
}
sample_var <- Vectorize(sample_var, vectorize.args = "alpha")
conf_int <- function(data,alpha){
a <- floor(alpha * n)
n <- length(data)
df <- n-2*a-1
data_t <- data[a:(n-a)]
t_mean <- mean(data_t)
t_quantile <- qt(p = alpha, df = df)
sw <- sample_var(data = data, alpha = alpha)
ul <- t_mean + t_quantile * sw / ((1-2*alpha)*sqrt(n))
ll <- t_mean - t_quantile * sw / ((1-2*alpha)*sqrt(n))
c(ll, ul)
}
Maybe someone sees the error?
EDIT:
Here I tried to construct the intervals using wilcox.test function, but I don't know whether it accurately constructs the interval for the trimmed mean. Furthermore, no matter which alpha I use, for the given data set, I get the same interval. So, I suppose that the subset argument is wrong.
set_seed(1)
data <- rnorm(100)
wilcox_test <- function(data, alpha){
n <- length(alpha)
a <- floor(alpha*n)+1
b <- n-floor(alpha)
wilcox.test(data, subset = data[a:b], conf.int = TRUE)
}

Answer 1

OK...with rnorm(100) and set.seed(1)
Close-ish...
set.seed(1) # note set.seed() is what you want here, I think.
data <- rnorm(100)
wilcox_test_out <- wilcox.test(data, subset = data[a:b], conf.int = .95)
summary(wilcox_test_out)
# Note the CI's are in wilcox_test_out$conf.int for further use should you need them
wilcox_test_out$conf.int