Suppose you are trying to estimate the percent of women in a city. Other things being equal, a simple random sample of 0.1% of the population of a city that has 2,000,000 people is ________ as a simple random sample of 0.1% of the population of a city that has 500,000 people. Fill in the blank with the best of the following choices.
about 2 times
"about 2 times as accurate" is the right answer
To find the best choice for the given question, we need to compare the sample size of the two cities.
For the first city, with a population of 2,000,000, a simple random sample of 0.1% would be:
0.1% * 2,000,000 = 0.001 * 2,000,000 = 2,000
For the second city, with a population of 500,000, a simple random sample of 0.1% would be:
0.1% * 500,000 = 0.001 * 500,000 = 500
Comparing the sample sizes, we observe that a sample of 2,000 is larger than a sample of 500. Therefore, the correct choice to fill in the blank is "larger" as a simple random sample of 0.1% of the population of a city with 2,000,000 people is larger than a simple random sample of 0.1% of the population of a city with 500,000 people.