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section8_4_solutions

# section8_4_solutions - Name 1 Time to respond for 911 calls...

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Name: 1) Time to respond for 911 calls was measured for 75 calls in two cities, C 1 and C 2. The results of the study were: Measure C1 C2 Sample size 75 75 Sample mean 5.4 6.1 Sample variance 1.57 2.54 This problem is solved exactly like Example 8.3 in the text. a) Estimate the difference in the mean response time for the two cities. The point estimate of μ 1 - μ 2 is y 1 - y 2 = 5 . 4 - 6 . 1 = - 0 . 7 b) Find a bound for the error of estimation. See Example 8.3 in the text. The standard deviation of the estimated difference is: σ Y 1 - Y 2 = radicalBigg σ 2 1 n 1 + σ 2 2 n 2 radicalBigg s 2 1 n 1 + s 2 2 n 2 = radicalbigg 1 . 57 75 + 2 . 54 75 = 0 . 234 The probability that the error of estimation is less than σ Y 1 - Y 2 2(0 . 234) = 0 . 468 is . 95. (two standard deviations) 2) An exit poll of 1 , 000 voters finds that 530 supported a certain candidate. a) Estimate the proportion of the voting population that supports the candidate. The estimator is ˆ p = y n = 530 1000 = 0 . 530 b) Find a bound for the error of estimation. The standard error for the estimator ˆ p is given by: σ ˆ p = radicalbigg pq n radicalbigg ˆ p (1 - ˆ p ) n = radicalbigg 0 . 53 · 0 . 47 1000 = 0 . 0158 With probability . 95, the error of estimation is less than 2 σ ˆ p = 0 . 0316

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3) Suppose Y is a single observation from an exponential distribution with unknown mean θ .
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