Question

. When we carry out a statistical test with significance level α = 5%, the probability of rejecting the null hypothesis when it is true is 5%. Suppose that we independently select 5 random samples of size 100, and for each sample carry out the same statistical test with significance level 5%. We know that the null hypothesis is true. What is the probability that we reject the null hypothesis at most once out of the 5 tests? (a) 0.02 (b) 0.19 (c) 0.77 (d) 0.81 (e) 0.98

Answer 1

probability of rejecting the null hypothesis, p = 0.05

As per binomial distribution,
P(X = r) = nCr * p^r * (1-p)^(n-r)

P(X <= 1) = P(X = 0) + P(X = 1)
= (1 - 0.05)^5 + 5C1 * 0.05 * 0.95^4
= 0.98

Option (e)