Question

A test of H 0 : µ = 19 versus H 1 : µ < 19 is performed using a significant level α = 0.01. The
value of the test statistic z = -1.68

a. Is H 0 rejected? Explain.

b. If the true value of µ =19, is the result of a type I error, a type II error, or a correct
decision?

c. If the true value of µ=0, is the result of a type I error, a type II error, or a correct
decision?

Answer 1

We have to test that

Test Statistics =Z=-1.68

a)

since test is left tailed so

P-Value =P(Z<-1.68)=0.046

since P value is higher than level of significance hence we failed to reject H0

so

H0 is failed to reject

b)

here true mean is 19 and we failed to reject hypothesis of true mean equal to 19 hence its

Correct Decision

c)

true mean is ZERO but we have accepted that true mean is 19 by not rejecting H0 Hence its

TYPE 2 error