Question

A quality expert inspects 420 items to test whether the population proportion of defectives exceeds .03, using a right-tailed test at α = .02.

(a) What is the power of this test if the true proportion of defectives is ππ = .05? (Round your intermediate calculations and final answer to 4 decimal places.)

Power:

(b) What is the power of this test if the true proportion is ππ = .06? (Round your intermediate calculations and final answer to 4 decimal places.)

Power:

(c) What is the power of this test if the true proportion of defectives is ππ = .07? (Round your intermediate calculations and final answer to 4 decimal places.)

Power:   

Answer 1

Solutions:-

Here first we compute the critical values of the proportion as:

For 0.02 level of significance we get from the standard normal tables that:

P( Z > 2.0537) = 0.02

Therefore the critical value of P here is computed as:

Therefore we reject the null hypothesis if the proportion comes out to be greater than 0.047

a) Now the power of the test is the probability that the null hypothesis is rejected given that it is false. For true proportion of 0.05, we get the power as:

P( p > 0.047)

Converting this to a standard normal variable, we get:

(B):- similar to the above case the power here is computed as:-

(C):- Similar to the above case the power here is computed as: