Los Angeles has about 4 times as many registered voters as S

Los Angeles has about 4 times as many registered voters as San Diego. A simple random sample of registered voters in each city is taken to estimate the percentage that will vote for school bonds. Others things being equal, a sample of size 4,000 taken in Los Angeles will be about (i) 4 times as accurate (ii) twice as accurate (iii) equally as accurate as a sample of size 1,000 taken in San Diego.

Solution

We know that Los Angeles has 4 times as many registered voters as San Diego. If the sample of same size is taken from both the cities, the accuracy rate will be 4 times better for Los Angeles.

But in the given question, we are taking 4000 registered voters from Los Angeles against 1000 registered voters from San Diego, therefore, the proportion in which the registered voters are taken from the total registered voters for each city is equal. Therefore, error in estimation will be equal for both the cities.

Hence, a sample size of 4000 taken in Los Angeles will be about equally as accurate as a sample size 1000 taken in San Diego