A study found that 73% of elementary students buy lunch at school at least once a month. How large a sample would be necessary to estimate the true proportion within 3 percentage points with 95% confidence?

A study is to be made to estimate the proportion of residents of a certain city and its suburbs who favor the construction of a nuclear power plant near the city. How large a sample is needed if one wishes to be at least 90​% confident that the estimate is within 0.06 of the true proportion of residents who favor the construction of the nuclear power​ plant?

Your state is considering raising the legal age for consumption of alcohol beverages. How large a sample size much be taken to make an estimate of the true portion of citizens who favor this move? The error should be no moe than 0.01 with 99% confidence.

A study is to be made to estimate the proportion of residents of a certain city and its suburbs who favor the construction of a nuclear power plant near the city. How large a sample is needed if one wishes to be at least 95​%  confident that the estimate is within  0.08  of the true proportion of residents who favor the construction of the nuclear power​ plant?

An environmental agency worries that many cars may be violating clean air emissions standards. The agency hopes to check a sample of vehicles in order to estimate the percentage with a margin of error of 5% and 95% confidence. To gauge the size of the problem, the agency first picks 40 cars and finds 8 with faulty emissions systems. How many should be sampled for a full investigation?

Nearly one-half of Americans ages 25 to 29 are unmarried. How large a sample is necessary to estimate the true proportion of unmarried Americans in this age group within 2 percentage points with 95% confidence?

A teacher worries her students are cheating. The teacher hopes to check a sample of students in order to estimate that percentage with a margin of error of 4​% and 90​% confidence. To gauge the size of the​ problem, the agency first picks 60 students and finds 12 are cheating. How many should be sampled for a full​ investigation?

A Gallup poll of 1487 adults showed that 43% of the respondents have Facebook pages.  Construct a 95% confidence interval for the proportion of adults who have a Facebook page.

An epidemiologist wants to estimate the proportion of residents in her city that carry the Hepatatis A virus. It is thought that the proportion is approximately 31%. How large a sample of residents should be taken to estimate the proportion who carry the Hepatitis A virus to within 10 percentage points with 98% confidence?

It is believed that 12% of Americans use a traditional antenna to watch network television.  How large a sample is needed to estimate the true proportion that use antennas with 95% confidence and within 2 percentage points? Show all work leading up to your answer below.