Econ120BCh3

Econ120BCh3 - Chapter 3 Answers 3.1, 3.6, 3.8, 3.10, 3.11,...

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Chapter 3 Answers 3.1, 3.6, 3.8, 3.10, 3.11, 3.12, 3.17, 3.18, 3.21 1. The central limit theorem suggests that when the sample size ( ) is large, the distribution of the sample average ( n Y ) is approximately 2 , Y Y N    with 2 . Y n 2 Y Given a population 100, Y we have 2 43 0, Y  (a) 100, n 2 2 43 100 043 , Y n Y  and 100 101 100 Pr ( 101) Pr (1.525) 0 9364 Y Y    (b) 64, n 2 2 43 64 64 0 6719, Y Y and 101 100 100 103 100 Pr(101 103) Pr 0 6719 0 6719 0 6719 (3 6599) (1 2200) 0 9999 0 8888 0 1111 Y Y      (c) 165, n 2 2 43 165 0 2606, Y n Y and 100 98 100 Pr ( 98) 1 Pr ( 1 Pr 0 2606 0 2606 1 ( 3 9178) (3 9178) 1 0000 (rounded to four decimal places) Y YY     6. (a) No. Because the p -value is less than 5%, 5 is rejected at the 5% level and is therefore not contained in the 95% confidence interval. (b) No. This would require calculation of the t -statistic for 5, which requires Y and SE () . Y Only one the p- value for 5 is given in the problem. 8   123 1000 1110 1.96 or 11 10 7.62. 10. (a) New Jersey sample size 1 100, n sample average 1 58, Y sample standard deviation 1 8. s The standard error of 1 Y is SE 1 1 8 1 100 0 8 . s n Y  The 95% confidence interval for the mean score of all New Jersey third graders is 11 1 1 96SE( ) 58 1 96 0 8 (56 432 59 568)       (b) Iowa sample size sample average 2 200, n 2 62, Y sample standard deviation 2 11. s The standard error of 12 is SE 22 64 121 100 200 ( ) 1 1158.
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Econ120BCh3 - Chapter 3 Answers 3.1, 3.6, 3.8, 3.10, 3.11,...

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