STAT231 Study Guide - Midterm Guide: Normal Distribution, Sampling Distribution, Central Limit Theorem
17 Jan 2014
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Ci = 0. 64 +- 3. 18*sqrt(109. 13/730) = (-0. 5895,1. 6695) By central limit theorem, the sampling distribution is approximately. Gaussian(p, sqrt(pq/n)) where p=13/106=0. 1226415 and sqrt(pq/n)= sqrt( (13/106 * ( 1-13/106) )/ 106)=. 03186063 p+- c* se(p) c= 1. 6449 from the gaussian distribution table di 0. 1226415 + 1. 6449 * . 03186063. Nobel prize winners in literature in general (including future ones). 106 nobel prize winners up to 2013 is the wrong answer. The population mean for past nobel prize winners is known and has no variation. z=( 0. 1226415 -0. 5) / sqrt(0. 5*0. 5/106) = -7. 77. The table only goes to z= 3. 59. p-value < 0. 01. There is very strong evidence against the null hypothesis that the percentage of women receiving the nobel price in literature is 50%. A t-test is incorrect because it computes sigma differently. In specifying the null hypothesis = or >= can be used. t= (77. 9 80 )/ (14. 1/sqrt(112)) = -1. 576. Under the null hypothesis t, has a t distribution with 111 degrees of freedom.
