Question

A researcher is interested in testing the hypothesis H0 : μ = 8 vs  H1 : μ > 8, using a sample of size 81. The population standard deviation is known to be σ = 5. The researcher decides to reject H0 if X  ≥  9. What is the significance level of this hypothesis test? Assume that the population is normal. Express your answer as a decimal (not as a percentage).

Answer 1

Solution:

Here, we have to find P(Xbar≥9)

P(Xbar≥9) = 1 - P(Xbar<9)

Z = (Xbar - µ)/[σ/sqrt(n)]

Z = (9 - 8)/(5/sqrt(81))

Z = 1.8

P(Z<1.8) = 0.96407

(by using z-table)

P(Xbar≥9) = 1 - P(Xbar<9)

P(Xbar≥9) = 1 - 0.96407

P(Xbar≥9) = 0.03593

Required significance level = 0.036