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.
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 reported 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.