Question

Suppose you will do five independent tests of the form H0: μ = 17 vs Ha : μ ≠ 17 all at the 5% α level. What is the probability of committing a Type 1 error and incorrectly rejecting a true null hypothesis with at least one of the five tests?

a. 0.01

b. 0.049

c. 0.05

d. 0.226

e. 0.7737

Answer 1

Solution:

given

n = 5, p = 0.05

We have to find P(X≥1)

P(X≥1) = 1 – P(X=0)

P(X=x) = nCx*p^x*q^(n – x)

Where, q = 1 – p = 1 – 0.05 = 0.95

P(X=0) = ⁵C₀*0.05^0*0.95^(5 – 0)

P(X=0) = 1*1*0.95^5

P(X=0) = 0.773781

P(X≥1) = 1 – P(X=0)

P(X≥1) = 1 – 0.773781

P(X≥1) = 0.226219

Correct Answer: 0.226