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Unformatted text preview: STA 103 Final Exam Spring 2008 I. H. Dinwoodie NAME Calculator and formula sheet allowed. STA103 Spring 2008 Final 1 1. (6 points) Two stocks had daily returns below in a 5 day week: day s1 s2 1 0.07 0.04 2 0.17 0.14 30.12 0.08 40.02 0.08 5 0.07 0.05 (a) What is the sample correlation? r=0.945 (b) Test the null hypothesis that the correlation ρ is 0, against the alternative H a : ρ > 0, at level α = . 01. Regression output from fitting the line s2=a + b*s1 was Parameter Estimates Estimate Std Error t Ratio Prob > t Intercept0.01373 0.016800.817 0.4737 s1 0.81559 0.16243 5.021 0.0152 Be sure to give the pvalue for the test and the test conclusion. Testing H : ρ = 0 versus H a : ρ > 0 is the same as testing for positive slope with H : β = 0 , H a : β > 0 (recall problem 15.3 and our discussion with JMP output). The output above is the way JMP presents regression, and the pvalue .0152 for the slope is twosided, although the notation is a bit misleading. Then the onesided pvalue is .0076, so at level .01, we reject ρ = 0 (.0076 < .01). STA103 Spring 2008 Final 2 Choose the best answer. (3 points each) 2. Women in 1975 in a certain city had normally distributed incomes that averaged μ W , with variance σ 2 . A sample of 100 was taken randomly and it was found that ¯ x = 19 . 0 and s x = 5 . 0 (in $1,000). Men in 1975 in that city had normally distributed incomes that average μ M , and a sample of 100 gave ¯ y = 21 . 5 and s y = 6 . 0. The standard error of the estimate 21 . 5 19 . 0 for μ M μ W is estimated by (a) 5.52 (b) 0.78 X (c) 0.50 (d) 0.55 (e) 0.05 3. A ski lift is designed to hold 20,000 pounds, and claims a capacity of 100 persons. Suppose the weights of all people using the lift have a mean of 190 pounds and with a standard deviation of 45 pounds. What is the probability that a random group of 100 people will total more than the weight limit of 20,000 pounds?...
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 Spring '08
 Dinwoodie
 Statistics, Normal Distribution, Probability, Standard Deviation

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