In [1]:

    

wald.test <- function (sample, lambda0, alpha) {
    # Conduct 2-sided wald test on sample
    # Return TRUE if H0 is discarded
    
    n <- length(sample)
    sampleMean <- mean(sample)
    sd <- sqrt(sampleMean/n)
    z <- qnorm(1-alpha/2)
    
    w <- (sampleMean - lambda0)/sd
    
    discardH0 <- FALSE
    if (abs(w) > z) {
        discardH0 <- TRUE
    }
    
    return(discardH0)
}


    

In [2]:

    

l0 <- 1
n <- 20
alpha <- 0.05


    

In [3]:

    

trials <- 100000
discards <- 0
for (i in 1:trials) {
    sample <- rpois(n, l0)
    discards <- discards + wald.test(sample, l0, alpha)
}
discards/trials


    

    
Out[3]:




0.05282

In [ ]: