Question

Suppose the American National Elections Studies agency (ANES) wishes to conduct a survey. It plans to ask a yes/no question to determine if those surveyed plan to vote for a certain candidate. One proposal is to randomly select 400 people and another proposal is to randomly select 1600 people.
Which of the following is true regarding the sample proportion ^p of "yes" responses?

a. The sample proportion from the sample of 400 is more likely to be close to the true population proportion, p.
b. The sample proportion from sample of 1,600 is more likely to be close to the true population proportion, p.
c. The sample proportion, ^p, in either proposal is equally likely to be close to the true population proportion, p, since the sampling is random.

Answer 1

Answer:

Since they use random sampling then we can conclude that the two estimators would be unbiased of the real parameter.

So then the best answer would be:

c. The sample proportion, ^p, in either proposal is equally likely to be close to the true population proportion, p, since the sampling is random.

Step-by-step explanation:

For this case we have a first sample size $n_1 =400$ and from this sample we have $x_1$ people who anwswer yes and the estimated proportion of yes is given by:

$\hat p_1 = \frac{x_1}{n_1}$

And let a second sample size $n_2 =1600$ and from this sample we have $x_2$ people who anwswer yes and the estimated proportion of yes is given by:

$\hat p_2 = \frac{x_2}{n_2}$

For this case we know that the true proportion is $p$

Since they use random sampling then we can conclude that the two estimators would be unbiased of the real parameter.

So then the best answer would be:

c. The sample proportion, ^p, in either proposal is equally likely to be close to the true population proportion, p, since the sampling is random.