please solve. show all your work in a separate paper.

8. The gestation period of humans has population standard deviation of 16 days. A simple random sample of 12 live births results in the following data. Construct a 95% confidence interval about the population mean. 266 l 270 | 277 | 273 | 253 | 275 | 261 | 260 l 270 l 269 | 252 l 277 9. A Sociologist wishes to estimate the percentage of U.5. population living in poverty. How large should the sample size be if she wants the estimate to be within 2 percentage points with a 99% confidence interval if she uses the 2003 estimate of 12.7% obtained from the American Community Survey. 10. A sociologist wishes to estimate the percentage of U5. population living in poverty. How large should the sample size be if she wants the estimate to be within 2 percentage points with a 99% confidence interval if she uses the 2003 estimate of 12.7% obtained from the American Community Survey if she does not use any prior estimate. 11. A school administrator is concerned about the amount of credit card debt college students have. She wishes to conduct a poll to estimate the percentage of full-time college students who have credit card debt of $2000 or more. How large a sample size should be obtained if she wishes the estimate to be within 2.5 percentage points with 95% confidence if a pilot study indicates the percentage is 34%? 12. A school administrator is concerned about the amount of credit card debt college students have. She wishes to conduct a poll to estimate the percentage of full-time college students who have credit card debt of $2000 or more. How large a sample size should be obtained if she wishes the estimate to be within 2.5 percentage points with 95% confidence if no prior estimates are used