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Statistics: Seat belted drivers, taste of PTC, spam in email

1) The proportion of drivers who use seat belts depends on things like age, gender, ethnicity, and local law. As part of a broader study, investigators observed a random sample off 117 female Hispanic drivers in Boston; 68 of these drivers were wearing seatbelts. Give a 95% interval for the proportion of all female Hispanic drivers in Boston who wear seat belts.

2) Does the above data give good reason to conclude that more than half of Hispanic female drivers in Boston wear seat belts?

3) PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inherited. About 75% of Italians can taste PTC, for example. You want to estimate the proportion of Americans with at least one Italian grandparent who can taste PTC. Starting with the 75% estimate for Italians, how large a sample must you collect in order to estimate the proportion of PTC tasters within ± 0.04 with 90% confidence?

4) Are you getting more spam in your personal email account? Suppose that 40% of adult email users would say "Yes." A polling firm contacts an SRS of 1500 people chosen from this population. If the sample were repeated many times, what would be the range of sample proportions who say "Yes," according to the 99.7 part of the 68-95-99.7 rule.

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