City A has 1,000,000 people; City B has 4,000,000 people. Suppose the goal is to try to predict the percent of Purple Party voters in a sample. Other things being equal, a simple random sample of 1% of the people in City A has about the same accuracy as a simple random sample of ________% of the people in City B. Pick the best option below to fill in the blank.
1- 0.1%
2- 0.25%
3- 0.5%
4- 0.75%
5- 1%
Which would give the same number in the sample?
I know 0.75% is wrong!
0.25 is the correct one
Thank you : D
To answer this question, we need to consider the population sizes of City A and City B.
City A has a population of 1,000,000 people, and the goal is to take a simple random sample of 1% of the people. To find out how many people are in a 1% sample, we can calculate 1% of 1,000,000:
1% of 1,000,000 = (1/100) x 1,000,000 = 10,000
So, a simple random sample of 1% of the people in City A would have 10,000 individuals.
Now let's consider City B, which has a population of 4,000,000 people. We want to find out what percentage of the people in City B would give us a sample size equivalent to that of City A (10,000 individuals).
To calculate this, we can set up a proportion:
(unknown sample percentage of City B) / 100 = 10,000 / 4,000,000
Cross-multiplying:
(unknown sample percentage of City B) = (10,000 / 4,000,000) x 100
Simplifying:
(unknown sample percentage of City B) = 0.25%
Therefore, a simple random sample of 0.25% of the people in City B would have about the same accuracy as a simple random sample of 1% of the people in City A.
Hence, the answer is option 2: 0.25%.