A student organization is planning to ask a sample of 50 students if they have noticed alcohol abuse brochures on campus. The sample percentage who say "Yes" will be reported. The organization's statistical advisor says that the standard deviation of this percentage will be about 7%.
a) What would the standard deviation be if the sample contained 100 students rather than 50?
b) How large a sample is required to reduce the standard deviation of the percentage who say "Yes" from 7% to 3.5%? Explain to someone who knows no statistics the advantage of taking a larger sample in a survey of opinion.