1. You are conducting some research for a beauty company and want to estimate the proportion of individuals who paint their nails at least once per month. You would like to be 95% confident that your estimate is within 3% of the true population proportion. How large of a sample size does your research require?

2. Giraffes travel in small groups and require excellent vision in order to detect predators. The eyesight of giraffes was studied in African Zoology (October 2013). The researchers measured a variety of eye characteristics for 27 giraffes native to Zimbabwe, Africa. One variable measured was eye mass (in grams). The study reported a random sample had a mean of 53.4 g and sample standard deviation of 8.6 g. If we know this data has an approximately normal distribution, use this information to find a 99% confidence interval for the true mean eye mass of giraffes native to Zimbabwe.

a. The best point estimate for this question is __________________ g. (Round to 1 decimal place, if needed.)

b. The critical t value is __________________ . (Round to 2 decimal places.)

c. The margin of error is _________________ . (Round to 3 decimal places, if needed.)

d. The final confidence interval is ____________ to __________ . (Round to one decimal place, and put the smaller number first.)

e. On your work upload paper, please answer the following: Based on the confidence interval, is it reasonable to believe that the true mean eye mass of giraffes native to Zimbabwe is greater than 52 grams? Why or why not?