Question

Gloria Chavez and Ronald Flynn are the candidates for mayor in a large city. You are planning a sample survey to determine what percent of the voters intend to vote for Chavez. You will contact a SRS of registered voters in the city. You want to estimate the proportion p of Chavez voters with 95% confidence and a margin of error no greater than 3%, or 0.03. How large a sample do you need? In the absence of any earlier poll to start from, use the guess p* = 0.5. n =__________

Answer 1

To estimate the proportion of Chavez voters with 95% confidence and a margin of error of 3%, a sample size of 1068 registered voters is needed.

Step-by-step explanation:

To determine the sample size needed for a simple random sample (SRS) survey where the proportion of voters for a mayoral candidate, Gloria Chavez, is to be estimated with 95% confidence and a margin of error of no more than 3%, we use the formula for calculating the sample size for a population proportion:

n = (Z^2*p*(1-p))/E^2

Here, Z is the z-score corresponding to the desired confidence level (1.96 for 95% confidence), p is the estimated proportion of the population voting for Chavez, and E is the desired margin of error. Since no prior data is available, we use p* = 0.5 (as it maximizes the required sample size, ensuring a conservative estimate) and E = 0.03. Plugging the values in the formula gives us:

n = (1.96^2*0.5*0.5)/(0.03^2)

n = (3.8416*0.25)/0.0009

n = 0.9604/0.0009

n = 1067.11

Since we cannot have a fraction of a person, we round up to the nearest whole number. Therefore, the sample size needed is:

n = 1068 registered voters