THE OHIO STATE UNIVERSITY
DEPARTMENT OF STATISTICS
STAT 4202 , INTRODUCTION TO MATHEMATICAL STATISTICS II
Midterm Exam 1
Instructions: This exam consists of three (3) problems - assessing material learned Within
chapters 9 and 10 of the course textbook. T
The aim is to find 99% condence interval for the difference of two populations.
The standard deviation of sarrples are given, use ftest.
The fomula to cormute the condence interval is shown beiow.
1 1 1 1
_ _ 5| I _ _ 5] 5
cfw_EddMM :1 +1: cfw_hallq'flxqr
Given are the heat-producing cap-a cities of coal from two mines cfw_in millions ofealeries
per ton) :
hneA:BU, 3330, 3430, T960, 3030
Minei. T890, T920, 830. 1350
The 99% condence interval for the difference of two true means is obtained frem the
Find the sarmle mean.
The sample mean is:
Find the sarmIe variance for the km data.
The sample variance is,
53 = Xh-Er
_ cfw_1.322333f +(1.922333f +-.-+cfw_1.9*2.2333)
Probability = cfw_1.99
a = I I199
at: = H.005
Substituting n=12, u :11]; and an =2,515 in the expression at rraxirmm enbr,
_ Zulu J;
Thua, the medical research writer can asaert with probability cfw_199 that thei
The probability density funeti on of normal distribution with parameters a and 02 is
f[x;,a,02)= 1 3 J ;03-:x-:03;y,02:=-U
L=E[X1,X2 . Xnmgj
'Wf *[Wf W?
5- J23? 5- J23? J- .323?
- HZ a
Compute the rst population raw moment as follows:
Compute the rst sample raw moment as follows:
Let I.,I=,.,.t_ be a random sample of size n tal-ten from a uniform distribution with a :1]
and ,3. Then, the rst sample raw moment is,
For I120. 0'1, from normal di stribution table we have 3m: =2_5'?5.
The 99% condence interval for the tme propmtion can be abtained Bram the below
. zapa) ,_ 50-3)
5 5 5+
. . A '18 . .
subshtut us 5' = Edi '13. 5 =100. and zm=2.5?5 m thr:
Given that. if Kis used as a point estimate of u. and ois known. the parotialsuilitsr is 1 a
that I; 111 , the absolute value of our en'or, will not exceed a an unied amount a when
Substituting 6': 2.5, = 2.5 and run =196 inthn above expression for the sa
13%) g: 2S3
n; 90 G) 1;- 0" 2- vs o W 135
ok" MY 01 no: 03' szzs vy .1 0' L 8m?
CZ) ELMV 3 WW 5 Z '. Z '
3 o 'XZ yw'm lxaqza - \mog
3 (M31 M 2x91
0 KL: L H ,_ 1W3,
(b Sum 96- 11553 1mm, wt SAM *0 n5u Pm, W
WK UmQMAokL M .WUJIL |5 v\0 quohmgL HM
Introduction to Mathematical Statistics II (4202)
Final Practice Exam
The exam is a closed book, closed notes and closed neighbor exam. You may use
four pages of notes (2 sheets), but no computer or communication devices, other
Introduction to Mathematical Statistics II (STAT 4202)
Extra Credit Problem (Optional)
Sec 13.7 uses the following test statistic
(fij eij )2
for both of the problems discussed in class where the null hypothesis of the first is
1. In a Gallup poll of 1,500 Americans in 1975 (from Gallup Opinion Index,
October 1975), 45% answered yes to the question Is there any area right around
herethat is , within a milewhere you would be afraid to walk alone at night? In
a similar 1972 poll o