(b) Did you use the CLT to answer part a? Why/why not? No. Since the original population is normal, X is exactly normal. 5. In the 1970s, the average age of a baseball player was estimated to be 32 years old, with a standard deviation of 3 years. This year, a sample of 49 baseball players gives a mean age of 31 years old. (a) Find a 95% confidence interval for the average age of a baseball player in the present day, assuming the standard deviation is still 3 years. = ± = ± = ± 84 .0 31 49 3 96 . 1 31 96 . 1 n X X (30.16, 31.84) (b) A sportswriter in the newspaper claims that the average age of baseball players is the same as it was in the 1970s. Is this claim supported by your data? Why or why not? No, it is not. The confidence interval from (a) gives a range of likely values for baseball players in the present. Since 32 does not appear in that interval, it is not likely that the average age of baseball players is the same as in the 1970s. (Indications are that it is actually lower) (c) Was the Central Limit Theorem required in this problem? Why/why not? Yes. The distribution of the original population was not specified, so the CLT tells us that the mean will be approximately normal for large enough n . Note: n = 49 was large enough.
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