# Exercises - Confidence Intervals for Proportions

1. You play a game and win 136 out of 270 times.

• Estimate the probability of winning the game.

• Find a 95% confidence interval for the probability of winning the game.

2. Find $z_{\alpha/2}$ for a 90% confidence interval for a proportion.

3. A CBS News/New York Times poll found that 329 out of 763 adults said they would travel to outer space in their lifetime, given the chance. Estimate the true proportion of adults who would like to travel to outer space with 92% confidence.

4. The Gallup Poll found that 27% of adults surveyed nationwide said they had personally been in a tornado. How many adults should be surveyed to estimate the true proportion of adults who have been in a tornado with a 95% confidence interval 5% wide?

5. A recent study indicated that 29% of the 100 women over age 55 in the study were widows.

• Find a 90% confidence interval for the true proportion of women over age 55 who are widows.

• How large a sample must one take to be 90% confident that the estimate is within 0.05 of the true proportion of women over age 55 who are widows?

• If no estimate of the sample proportion is available, how large should the sample be to be 90% confident that the estimate is within 0.05 of the true proportion?