If a bootstrap confidence interval (CI) can be interpreted as a standard CI (e.g., the range of null hypothesis values that cannot be rejected) [also stated in this post]. Is it ok to derive a p-value from a bootstrap distribution like this? When the null hypothesis is $H_0: \theta=\theta_0$ and a bootstrap ($1-\alpha$)$\times 100\%$ CI is ($\theta_L$, $\theta_U$)$_{\alpha}$. The p-value is $\alpha$ corresponding with $\theta_U=\theta_0$ or $\theta_L=\theta_0$.

This post also describes examples of converting CIs to p-values, but I do not completely understand...

The following code derives a p-value from the percentile CI of the slope parameter of a linear regression model, and it can be applied to other types of CIs. If this is not ok, what is the appropriate way to compute a p-value, e.g., associated with the percentile CI? If the code below is ok, can it be described as a bootstrap hypothesis test (e.g., when describing it in a paper)?

# generate hypothestical data
x <- runif(20,10,50)
y <- rnorm(length(x),1+0.5*x,2)

model <- lm(y~x)
plot(x,y)
abline(model)

params    <- coef(model) 

nboot <- 2000
eboot <- matrix(NA,nboot,2)
for(i in 1:nboot){
 booti <- sample(1:length(x),replace=T)
 eboot[i,] <- coef(lm(y[booti]~x[booti]))
}

# 95% CI
quantile(eboot,c(0.025,0.975))  # percentile CI
params[2]*2-quantile(eboot,c(0.975,0.025)) # basic CI

# null hypothesis
null <- 2 

get.p <- function(x,null){
 ifelse(null>quantile(eboot,0.5),return(null-quantile(eboot,1-x/2)),return(null-quantile(eboot,x/2)))
}

#x <- seq(0,1,length=100)
#plot(x,get.p(x,null),type="l")
(p <- uniroot(get.p,null=null,c(0,1))$root)  # p-value
#abline(v=p,h=0)

If a bootstrap confidence interval (CI) can be interpreted as a standard CI (e.g., the range of null hypothesis values that cannot be rejected) [also stated in this post]. Is it ok to derive a p-value from a bootstrap distribution like this? When the null hypothesis is $H_0: \theta=\theta_0$ and a bootstrap ($1-\alpha$)$\times 100\%$ CI is ($\theta_L$, $\theta_U$)$_{\alpha}$. The p-value is $\alpha$ corresponding with $\theta_U=\theta_0$ or $\theta_L=\theta_0$.

This post also describes examples of converting CIs to p-values, but I do not completely understand...

The following code derives a p-value from the percentile CI of the slope parameter of a linear regression model, and it can be applied to other types of CIs. If this is not ok, what is the appropriate way to compute a p-value, e.g., associated with the percentile CI? If the code below is ok, can it be described as a bootstrap hypothesis test (e.g., when describing it in a paper)?

# hypothestical data
x <- runif(20,10,50)
y <- rnorm(length(x),1+0.5*x,2)

model <- lm(y~x)
plot(x,y)
abline(model)

params    <- coef(model) 

nboot <- 2000
eboot <- rep(NA,nboot)
for(i in 1:nboot){
 booti <- sample(1:length(x),replace=T)
 eboot[i] <- coef(lm(y[booti]~x[booti]))[2]
}

# 95% CI for the slope
quantile(eboot,c(0.025,0.975))  # percentile CI
params[2]*2-quantile(eboot,c(0.975,0.025)) # basic CI

# null hypothesis
null <- 0.5

get.p <- function(x,null){
 if(null>quantile(eboot,0.5)) return(null-quantile(eboot,1-x/2))
 if(null<quantile(eboot,0.5)) return(null-quantile(eboot,x/2))
}

#x <- seq(0,2,length=100)
#plot(x,get.p(x,null),type="l")
(p <- uniroot(get.p,null=null,c(0,1))$root)  # p-value
#abline(v=p,h=0)