HW19_SOL - 261 90 1 30 29 30 1 30 29 30 1 3 30 1 n n n 3 ....

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
ECO220Y: Homework, Lecture 19 – SOLUTIONS (1) The rule of thumb requires that the entire interval defined by p ± 3( p (1- p )/n) 0.5 has to be contained between 0 and 1. Since p=8/30=0.27, n=50, the interval is [0.08,0.46], which falls within [0,1]. Thus, sampling distribution of the proportion is reasonably approximated by normal distribution. (2) 0192 . 0 ) 07 . 2 ( 0628 . 0 27 . 0 4 . 0 50 20 ˆ Z P Z P P P (3) Following the same argument as (1), we can check the rule of thumb. Since p=1/30=0.03, n=50, the interval is [-0.04,0.10]. Since this is not contained between 0 and 1, we cannot reasonably approximate the sampling distribution of the proportion by normal distribution. (4) 1836 . 0 30 29 50 . (5) We consider the widest interval allowed in the rule of thumb, which is [0,1]. So find n such that left end of the interval is 0 or n such that the right end of the interval is 1.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 261 90 1 30 29 30 1 30 29 30 1 3 30 1 n n n 3 . 90 29 30 29 30 1 30 29 30 1 3 30 1 n n n We only needed to check lower endpoint because this distribution is positively skewed. Even with a sample size of only 1, we would have no trouble with the upper endpoint. Hence we need a sample size of at least 261. (6) Sample proportion Expected value Standard error (se) Approx. normally distributed? of maroon balls (1s) 0.267 0.063 Yes of green balls (2s) 0.167 0.053 Yes of purple balls (3s) 0.033 0.025 No of pink balls (4s) 0.067 0.035 No of yellow balls (5s) 0.200 0.057 Yes of orange balls (7s) 0.100 0.042 No of blue balls (9s) 0.133 0.048 No...
View Full Document

Ask a homework question - tutors are online