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QUESTION:

The next three questions refer to the following information:

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.

Question 2 of 6

Question 2

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Which of the following is true regarding the sample proportion p-hat, of "yes" responses?

ANSWER:

The sample proportion from the sample of 900 is more likely to be close to the true population proportion, p.

Good job! The larger the sample size, the closer we expect the sample proportion to be to the true population proportion. Intuitively, this makes sense, since the larger the sample, the more it is “like the population.” More formally, since the standard deviation of the sampling distribution of the sample proportion p-hat is: p(1−p)n , it decreases as the sample size increases. This means that for larger sample sizes, the possible values of p-hat are less spread out and therefore more likely to be closer to their mean, which is the population proportion, p.

Posted by Cleveland on September 22, 2024
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