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STA 103 Exam 2 Spring 2008 I. H. Dinwoodie NAME Calculator allowed, closed book.

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STA103 Spring 2008 E2 1 Circle True or False. (1 point each) 1. The population of American women in 1975 had incomes that averaged μ = 10, with standard deviation σ = 7 (in units of \$10,000). A random sample of 1,000 women was drawn. (a) T The sample mean is an unbiased estimator of μ . (b) F The sample variance s 2 is a biased estimator of σ 2 . (c) F The probability distribution of the sample mean ¯ X has a density that resembles the probability histogram of the population. (d) F The variance of the sample mean is the same as the variance of the population. (e) F A 95% confidence interval for μ is wider than a 99% confidence interval for μ . (f) F A 99% confidence interval for μ will always contain the mean μ . (g) F The mean squared error (MSE) of the sample mean for estimating μ is σ 2 . (h) F The mean squared error (MSE) of the sample mean for estimating μ is greater than the MSE of a single draw. (i) 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. (j) T The probability histogram of the sample should resemble the prob- ability histogram of the population.
STA103 Spring 2008 E2 2 2. (4 points) At a large Midwest factory, 4 men and 4 women on the assembly line

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