Question

Suppose 10% of students are veterans and 130 students are involved in sports. How unusual would it be to have no more than 5 veterans involved in sports? (5 veterans is about 3.8462%)

1.)When working with samples of size 130, what is the mean of the sampling distribution for the proportion of veterans?

2.)When working with samples of size 130, what is the standard error of the sampling distribution for the proportion of veterans?

3.)Compute P( ˆ p ≤ p^≤ 0.038462).

Answer 1

e denotes P Let pdportion population of veterans. 10 1. thar Given are vekerans students 0I0 P- sample size he HeRe i s n 130 . denotes he Let Sample pmoportion of veterans The mean ot Hhe dishmibution Sampling for he sample veterans poportion i s P r OIO

2 The standard ermor SampLing for the of the dishmbution veterans proportion of is pli-p) 010 x (1-0.o 130 O 0263112 3> By central Limit heorem, Know we he samp Le :f hat Size is suffieiently arge hat both np 10 So n11-P)10 , then and

PNI M ) n 130 P -0.10 He re np =130 x 010 13 10 nl1-P) -130 x(1-0.10) 1l 7 10

PANLO10, (0 02631 2) Now, 003 84 6 2 PA P-0.10 0 026312 O038162 - 010 0.026 31 2 PZ-2 34 Let Z O 0 26312 then ZN(0,1)

- -2 34 -1 (2 34) he cdf of is N(0,1). 109904 =00 0 96 For any KO (k) . 7 l-K)- hat Know We result 1s observed : f he unusual pnobability ob1aining he resulh 0 O 5 i s han Less

Here PP003 846 2 ) 2 0.05 0.0096 be unusual So it Would han have more no involved veterans sports in