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Unformatted text preview: STAT 226 HOMEWORK 4 ANSWERS Show all your work for full credit and print any necessary JMP output! 1 . a) A parameter is a number that describes the population. It is fixed and generally we do not know its value. A statistic is a number that describes a sample. The value of a statistic can change from sample to sample. We often use a statistic to estimate an unknown parameter. b) Answers will vary. There should be a source, article, and a parameter and statistic that make logical sense. Example: I am interested in knowing how much it will cost me to get a haircut. Population: All places in Ames that cut hair. Parameter: the average cost of hair-cutting at all of those places. Sample: Places in Campustown that cut hair. Statistic: The average cost of hair-cutting in Campustown. 2 . Table a) The first person would be Richards (23), the second would be Gates (12) b) The sample would be: Liu, Sanchez, Collins, Gonzalez 3. Box Offices . (a) As shown in the histogram, the distribution of the domestic gross of all 1,986 movies is heavily skewed to the right with quite a few extreme outliers. (b) The mean is = 27.769587 Million Dollars. Because we considered the 1,986 movies released between 1990 and 1999 as the population of interest, this mean corresponds to the population mean. (c) Three samples of size 30 yielded means 1 x = 22.45, 2 x = 32.31, and 3 x = 41.03. None of these individual means are very close to , although 1 x and 2 x are considerable closer to than 3 x . The third sample contained two movies Saving Private Ryan (1998) with $216.1 and The Lost World: Jurassic Park (1997) with $229.1 which we can consider outliers causing the sample mean to be pulled up. The histogram of the third sample is given below. (d) The Central Limit Theorem (CLT) states that as the sample size increases, the sampling distribution of the sample mean will converge to a Normal distribution. The shape of the original distribution does not matter for this result, only to the extent of how large of a sample size is necessary for the sampling distribution to approach Normality. In general, the further away the distribution is from Normal (e.g. skewed, extreme outliers in the population), the larger the necessary sample size for the CLT to apply....
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- Fall '08