Has the law requiring bike helmet use failed?

Yankelovich Partners conducted a survey of bicycle riders in the United States. Only 60% of the nationally representative sample of 1020 bike riders reported owning a bike helmet.

Source: http://www.cpsc.gov/library/helmet.html

a. Find the 95% confidence interval for the true proportion p for a binomial experiment of 1020 trials that resulted in an observed proportion of 0.60. Use this to estimate the percentage of bike riders who report owning a helmet.

b. Based on the survey results, would you say there is compliance with the law requiring bike helmet use? Explain.

Suppose you wish to conduct a survey in your city to determine what percent of bicyclists own helmets.

Use the national figure of 60% for your initial estimate of p.

c. Find the sample size if you want your estimate to be within 0.02 with 95% confidence.

d. Find the sample size if you want your estimate to be within 0.04 with 95% confidence.

e. Find the sample size if you want your estimate to be within 0.02 with 90% confidence.

f. What effect does changing the maximum error have on the sample size? Explain.

g. What effect does changing the level of confidence have on the sample size? Explain.