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Unformatted text preview: EXERCISES IN STATISTICS Series A, No. 8 1. The value of the mean of a random sample of size 20 from a normal pop- ulation is x = 81 . 2 Find the 95% confidence interval for the mean of the population on the assumption that the variance is V ( x ) = 80. Answer. We have x = 81 . 2, V ( x ) = 80 , n = 20 and a confidence level of Q = 0 . 95. The confidence interval is derived from the following probability statement: P x n x + n = Q. The values of corresponding to Q = 0 . 95 is = 1 . 960. Therfore the confind- ence interval is x n = 81 . 2 1 . 96 80 20 = [77 . 28 , 85 . 12] . 2. Let x be the mean of a random sample of size n from an N ( , 2 ) popu- lation. What is the probability that the interval ( x 2 / n, x + 2 / n ) includes the point ? Answer. We have P x 2 n x + 2 n = P 2 z = x / n 2 , where z...
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This note was uploaded on 03/02/2012 for the course EC 2019 taught by Professor D.s.g.pollock during the Spring '12 term at Queen Mary, University of London.
- Spring '12