1. A recent survey of 110 individuals revealed that 45 thought they were worse off financially than a year ago. Find a 90% confidence interval for the true proportion of individuals that feel they are worse off financially. 2. A company has a new process for manufacturing large artificial sapphires. In a trial run, 36 sapphires are produced, with a sample mean weight of 6.75 carats, and a sample standard deviation of 0.33 carats. Find a 95% confidence interval for the mean weight of all sapphires produced with the new process. 3. A researcher wants to find the weight of adult male sheep. A random sample of 37 adult male sheep indicated a standard deviation of the sheep weight to be 15.8 pounds. How many male sheep should be included in a sample to be 90% sure that the sample mean weight of all adult male sheep is within 2.5 pounds of the population mean weight? 4. A medical researcher wants to find the percentage of females who take vitamins. He wishes to be 95% confident the estimate is within 2% points of the true proportion. A recent study of 180 females showed that 25% took vitamins. How large should the sample size be