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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 3-0.12 -0.08 4-0.02 -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| Intercept-0.01373 0.01680-0.817 0.4737 s1 0.81559 0.16243 5.021 0.0152 Be sure to give the p-value 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 p-value .0152 for the slope is two-sided, although the notation is a bit misleading. Then the one-sided p-value 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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