A local newspaper claims that in a population of voters in a certain region, 40% are in favour of a particular political party. Four hundred (400) randomly selected voters are asked if they support that political party.

(a) (2 pts) Verify that the sample proportion ^p computed from samples of size meets the condition that its sampling distribution be approximately normal.

(b) (2 pts) Given that a newspaper's claim is true, would you be surprised if only 100 randomly selected

voters out of 400 support that political party? Why?

(c) (4 pts) Find the required sample size if we want our estimate to be within 0:05 of the population proportion with probability 0.95 in the following two cases:

1. The newspaper's claim is true, that is p = 0:40.

2. We don't have any prior knowledge about the true population proportion.