A marketing firm samples 150 residents of a certain town to determine the sample proportion p that

Question:

A marketing firm samples 150 residents of a certain town to determine the sample proportion ̂p that have seen a new advertisement. A test of the hypotheses H0: p = 0.4 versus H1: p

a. Find the critical value zα.

b. Find the value of ̂p whose z-score is −zα. Call this value p∗.

Note that the population standard deviation is

c. We want to find the power against the alternative p1 = 0.3.
The power is the area to the left of p∗ under the assumption that the true proportion is p1 = 0.3. Find the power. [Note that the standard deviation is now