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Unformatted text preview: Statistics 103: Lab 7 For each confidence interval problem below be sure to first compute the estimate and the (esti- mated) standard deviation of the estimate to get a quick and easy idea of where the true population parameter is. Then follow up by computing the technically sound confidence interval (and ask yourself if you are ever mislead by the quick and easy method). LAB PROBLEMS 1. To establish the authenticity of an ancient coin, its weight is often of critical importance. Given that four experts independently weighed a Phoenician tetradrachm and got 14.28, 14.34, 14.26, and 14.32 grams, construct a 95% confidence interval for the actual weight of this coin. (Such repeated measure- ments of one and the same object can usually be look upon as a sample from a normal population.) answer: (14.24, 14.36) 2. In California, the mean alcohol by volume percent- age (ABV%) of a batch of beer must be within 0.2 of the ABV% printed on the label. This is of major concern to microbreweries, since batches of beer tend to be highly variable. Suppose the brew- ers happen to be worried about a particular batch of their strongest beer, labeled with 10.2% ABV. They decide to open three 4-packs from that batch and measure the ABV%. They find that the bottles had a mean of 10.32% with a standard deviation of 0.11%. Give a 95% confidence interval for the batch mean ABV%. Do they have reason to be concerned about the batch? answer: (10.25, 10.39); No 3. Suppose we are comparing freshmen and seniors at UC Davis on hours spent studying per day. We pick a sample of 21 freshmen and 11 seniors. For freshmen, the mean was 3 and the variance was 0.9. For seniors, the mean was 2 and the variance was 1.2. Construct a 90% confidence interval on the difference between means (freshmen - seniors)....
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