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# e2Aanswersfall07 - STA 103 Exam 2a Fall 2007 I H Dinwoodie...

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STA 103 Exam 2a Fall 2007 I. H. Dinwoodie NAME Calculator allowed, closed book.

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STA103 Fall 2007 E2a 1 Circle True or False. (1 point each) 1. The population of American men in 1975 had incomes that averaged μ , with variance σ 2 . A random sample of 1000 men was drawn to estimate μ and σ 2 . (a) T The probability histogram of the sample should resemble the prob- ability histogram of the population. (b) F The sample mean is a biased estimator of μ . (c) F The sample variance is a biased estimator of σ 2 . (E( S 2 ) = σ 2 ) (d) F The probability distribution of the sample mean ¯ X has a density that resembles the probability histogram of the population. (e) F The variance of the sample mean is the same as the variance of the population. (Var( ¯ X ) = σ 2 / 1000) (f) F A 95% confidence interval for μ is wider than a 99% confidence interval for μ . (g) F A 99% confidence interval for μ will always contain the mean μ . (h) F The mean squared error (MSE) of the sample mean for estimating μ is σ 2 . (MSE( ¯ X ) = σ 2 / 1000) (i) F The mean squared error (MSE) of the sample mean for estimating μ is greater than the MSE of a single draw. (j) T The sample mean has a probability distribution that is bell-shaped and is more tightly concentrated around μ than the distribution of the population. (Central Limit and the MSE of ¯ X apply)
STA103 Fall 2007 E2a 2 2. (4 points) In a large American university in 1969, 3 men and 4 women profes- sors were sampled independently, yielding the annual salaries given below (in thousands): Women Men 8 13 10 12 16 23 15

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