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What Percentage of the Earth’s Surface is Water? Make a small dot on your thumb. Toss the globe beach ball from person to person, determining whether your dot was in water or land. Sample Data: Water Land Tally 1. We are trying to determine (estimate!) the true proportion p of water on the Earth’s surface. We have just taken a sample size n = _______ with X = _____ successes. Therefore, our sample proportion p = ______. 2. Even though we only have one p , what do we know about the distribution of all the p ' s from a population with a true proportion p? The p ' s will be approximately normal with a mean of p and a standard deviation of p(1 p) . n 3. Can we calculate the mean and standard deviation of the p ' s from this population? Why or why not? No, because we do not know the value of p. 4. Is there a logical way to deal with this issue? Yes, we will need to estimate p with p . 5. Since we are probably convinced that our one p is not correct, let’s put a “buffer zone” around our estimate. Is there a logical way to determine the size of the “buffer zone”? What will the size of the “buffer zone” necessarily be related to? Yes, using our knowledge about the sampling distribution of p . The size will certainly be related to the sample size AND how confident we want to be. 6. Calculate an estimate of p that you would be confident to share. p z* p(1 p) p(1 p) p p z* n n