Question

A social scientist wishes to conduct a survey. she plans to ask a yes/no question to a random sample from the u.s. adult population. one proposal is to select 100 people; another proposal is to select 900 people. which of the following is true regarding the sample proportion , of "yes" responses?

a) the sample proportion from the sample of 100 is more likely to be close to the true population proportion, .
b) the sample proportion from the sample of 900 is more likely to be close to the true population proportion, .
c) the sample proportion in either proposal is equally likely to be close to the true population proportion, ,
d) since the sampling is random. it is impossilbe to say from the information given.

Answer 1

The option that is true regarding the sample proportion , of "yes" responses is b) the sample proportion from the sample of 900 is more likely to be close to the true population proportion.

A larger sample size is known to be one that is said to be a more accurate estimate of the population proportion. The Central Limit Theorem states that the sample proportion will be approximately normally distributed with a mean equal to the population proportion and a standard deviation that is inversely proportional to the square root of the sample size.

So, This is one that mean that as the sample size increases, the standard deviation of the sample proportion decreases, making it more likely that the sample proportion will be close to the true population proportion.