1. People in a large population average 60 inches tall. You will take a random sample and will be given a dollar for each person in your sample who is over 65 inches tall. For example if you sample 100 people and 20 turn out to be over 65 inches tall, you will get $20. Which is better: a sample of size 100 or a sample of size 1,000? Chose one and explain. Does the law of averages relate to the answer you give?
2. Polls showed the two main candidates in the 2004 presidential election were nearly tied on the day before the election. To predict the winner a newspaper would like to have a poll that has margin of error of less than 1%. Roughly how large a sample would be needed for such a poll?
1) This is an interesting question. In a normal population, the height of individuals would follow a bell curve, where the middle of the curve (the highest point) would be at 60 inches. Then, we would get people who are taller or shorter than 60 inches, as you move away from the middle. If you look at the rules of the bell curve, 68% of the population would be within 1 standard deviation of 60 inches, 95% would be within 2 standard deviations, and 99% would be ...
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