# Question

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.

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.

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