Question Completion:
California (population about 40 million) has about twice as many people as New York State (population about 20 million). Without calculation, pick the correct option and explain your choice.
If the underlying population SDs are equal, a simple random sample of 1000 people in California is
(i) about half as accurate
(ii) about 1/V2 times as accurate
(iii) about as accurate
(iv) about V2 times as accurate
(v) about twice as accurate
as a simple random sample of 1000 people in New York State.
Answer:
If the underlying population SDs are equal, a simple random sample of 1000 people in California is
(i) about half as accurate
as a simple random sample of 1000 people in New York State.
Step-by-step explanation:
Since the population of California is about 40 million, which is twice as many people as in New York State (approximately 20 million), in taking a sample size, that of California supposed to be as twice as New York's.
Therefore, if the random sample of 1,000 people is taken from California, just as a random sample of 1,000 people is also taken from New York State, we can conclude that the accuracy of population standard deviation of California will be about half as accurate as the standard deviation of New York's population.
This is because accuracy is enhanced by a larger sample size. This means that if the sample size of California is 2,000, the SD would have been equally as accurate as New York's.
