Question

A researcher performs three independent hypothesis tests each at the 5% significance level.

Determine the probability of observing at LEAST one Type I Error. (Round your final answer to the nearest hundredth of a percent)

Answer 1

x ~ Binomial (3, 0.05)

The binomial distribution function.

$P(x=k) = ^nC^k(p^k)(1 – p)^{n-k} \\ P(x≥1) = 1 -P(x=0) \\ = 1 -^3C^0(0.05)^0(0.95)^3 \\ = 1 -0.8573 \\ = 0.1427$

Answer: 14.27 %