Diamonds are classified according to carat (weight), clarity, color, and cut. The color of a diamond is classified as D, E, F, G, H, or I. Of the 308 diamond stones that were listed for sale on the open market in Singapore's Business Times on February 18, 2000, 61 were classified as "H" color.
a. Taking the diamonds listed in the advertisement as a simple random sample of all diamonds available for sale on the open market, find a 95% confidence interval for the proportion of diamonds that are classified as "H" for color
b. Using your confidence interval, is it reasonable to assume that 24% of diamonds on the open market are classified as "H" for color? Explain why or why not?
c. Using the information from the advertisement as a preliminary sample, what size sample would be needed to create a sample with a margin of error of .03 at 95% confidence?