Question

4.7 The R&D department of a company has developed a new home screening test for diabetes. A demonstration of the type of results that may occur was mandated by upper management. Simulate the probability of obtaining at least 24 positive results and 6 negative results in a set of 30 results. The researchers state that the probability of obtaining a positive result is 80%.

1. Let a two-digit number represent the outcome of running the screening test. Which numbers should represent a positive result?

2. Approximate the probability of obtaining at least 24 positive results and 6 negative results in a set of 30 results by generating 10,000 sets of 30 two-digit numbers.

Answer 1

An R Script can work for solving this problem as:

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## Simulation of a list of 10000 random samples with TRUE (+ve) and FALSE (-ve)
rnd <- list()
for(i in 1:10000){
rnd[[i]] <- sample(c(T, F), size = 30, replace = T, prob = c(0.8, 0.2))
}

## Generate a vector to obtain the respective 2-digit numbers of TRUEs (+ve) in the simulations
asgn.num <- c()
for(i in 1:10000){
asgn.num[i] <- sum(rnd[[i]])
}

## Unique two digits are
unique(asgn.num)

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(i) For first question for positive results we can assign the numbers:

22, 26, 24, 21, 25, 28, 23, 27, 19, 30, 20, 29, 17, 18, 16, 15, 14

(ii) The ratio for approximate probability can be given by the R code:

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sum(asgn.num >= 24)/10000

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which is always near by 0.60.