Question

Gloria Chavez and Ronald Flynn are the candidates for mayor in a large city. We want to estimate the proportion p of all registered voters in the city who plan to vote for Chavez with 95% confidence and a margin of error no greater than 0.03. How large a random sample do we need?

Answer 1

Answer: 832

Explanation:

The sample size needed to estimate the proportion of all registered voters in the city who plan to vote for Chavez with a 95% confidence level and a margin of error of 0.03 is 832.

To calculate the sample size, we use the following formula: n = (1.96^2)p(1-p) / (margin of error)^2.

In this case, we can assume the population proportion p is 0.5, which is the midpoint between 0 and 1, so we can plug in 0.5 for p. We also plug in 0.03 for the margin of error.

After solving for n, we get 832 as the sample size needed. This means that we need a sample of 832 randomly selected registered voters in the city in order to estimate the proportion of all registered voters in the city who plan to vote for Chavez with 95% confidence and a margin of error no greater than 0.03.