Vaccines protect billions of people around the world. They have completely got rid of one disease - smallpox - and are bringing the world close to eliminating others, such as polio. But some other diseases, such as measles, are making a resurgence and experts say people avoiding vaccines, fueled by fear and misinformation, is one of the main causes. So much so that the World Health Organization now lists vaccine hesitancy as one of the top 10 threats to global health.

A new Wellcome Global Monitor https://wellcome.ac.uk/reports/wellcome-globalmonitor/2018?utm_source=link_newsv9&utm_campaign=item_259574&utm_medium=copy asked people if they felt "Vaccines are important for children to have". 74% of 767 Americans surveyed, including 73% of 408 American men surveyed and 75% of 359 American women said they strongly agreed with this statement. (Results were based on telephone interviews conducted in a random sample of adults, aged 18 years and older, living in all 50 U.S. states and the District of Columbia.)

a) Use the formula: 2 (100) to determine the margins of error for

(i) All Americans,

(ii) American Men and

(iii) American Women who strongly agree that vaccines are important for children to have. Use two decimal places.

b) What are the 95% confidence intervals for

(i) All Americans,

(ii) American Men and

(iii) American Women who strongly agree that vaccines are important for children to have?

c) How certain can we be that more American women strongly agree that vaccines are important for children to have than American Men? Explain.