HW 5 FOR STAT601, fall, 2012
1) 6.14
Comment on the shape, what distribution is a reasonable t?
2) 6.30
Comment on the shape, same as the stef and leaf? Is the number of bins chosen reasonable?
3) 6.46
4) 6.96
5) 6.99
6) 6.101
7) 7.15
8) 7.20
9) 7.22
10)
HW 12 FOR STAT601, Fall, 2012, PRACTICE ONLY, NOT TO HAND IN
1) An experiment is run to compare the tar content (mg) of 3 dierent brands of cigarettes. 10,
20 and 20 cigarettes are measured for brands A, B and C. The respective averages are (all in
millig
Solution to HW10:
^ 11-18 0
^ ^ ^ + 1 x = ( y - 1 x ) + 1 x = y
11-19 a) The slopes of both regression models will be the same, but the intercept will be shifted. ^ b) y = 2132.41 - 36.9618 x
^ 0 = 2625.39 ^ 1 = -36.9618
Problem 3.
a) x
vs.
^ 0 = 2132.41
HW 11 FOR STAT601, Fall, 2012 (Due November 28)
1) For the colon cancer data on the dostat site:
a) Compute the correlation coecient between meat eaten and colon cancer rates for the 23
given countries.
b) Viewing the given countries as a random sample fr
Solution to HW11: 1. (a) From the SAS output,
= R 2 = 0.7276 = 0.8530
(b) The 95% confidence interval for
r
is
t n 2, / 2
1 2 n
Here,
n = 23
and
= 0.05 , so t n 2, / 2 = 2.079614 .
1 0.8530 2 23
n 3 n 3
The confidence interval will be
0.8530 2.079614
Solution to HW9:
5-18. They are not independent, since the joint pdf can not expressed as the product of two function related to x and y , respectively.
c
0
3 x+2
( x + y)dydx = xy +
3
y2 2
x+2
dx
x
= x( x + 2) +
0 3
3
[
x
0
( x+ 2)2 2
- x2 -
x2 2
]dx
=
Practice problems on last topics:
1) We want to analyze the pain data described in Pain Study on the webpage.
a) Does there appear to be a dierence in pain thresholds between students and dancers?
b) Does there appear to be a dierence in pain thresholds b
HW 1 FOR STAT601, Fall, 2012
1) 2.2
2) 2.16
3) 2.21
4) 2.62
5) 2.69
6) 2.75
7) 2.115
8) 2.123
9) For a given component, data has shown that the chance of survival beyond 50 hours is .89, and
the chance of survival beyond 60 hours is .80. What is the chanc
HW 2 FOR STAT601, Fall, 2012
1) 3.24
2) 3.27
3) Find the mean and variance for the p.d.f in 3.24
4) 3.47 and: whats the variance of X?
5) 3.64 a) and b)
6) 3.79
7) 3.87
8) Each word in the Oxford English Dictionary (OED) has a 0.001% chance of being a typ
Hints/Solutions to the Practice Problems:
1) The main eects for job is signicant, but those for sex and job by sex interaction are not. Thus we
see that the dancers experience less pain than the students and this is the only signicant eect.
2) The null hy
Solution to HW1 2-2.
Let "e" denote a bit in error Let "o" denote a bit not in error ("o" denotes okay)
eeee, eoee, oeee, ooee, eeeo, eoeo, oeeo, ooeo, S = eeoe, eooe, oeoe, oooe, eeoo, eooo, oeoo, oooo
2-16.
memory
4
8
12
disk storage 200 300 400 200 30
HW 10 FOR STAT601, Fall, 2012
1) 11.18
2) 11.19b
3) The census bureau wants to know the relationship between 2000 and 2010 populations in districts in
the U.S. They sample four districts whose 2000 populations were 19.1, 17.2, 5.2 and 10.4 with correspond
HW 8 FOR STAT601, Fall, 2012
1) For the data on heights of men and women verify (by hand) the values of the pooled two
sample t-statistic and the unpooled two sample t-statistic, and verify the p-values (as accurately
as possible) from the t-table.
2) We
Solution to HW4
7-3
X = 75.5 psi X =
n
P ( X 75 .75 ) = P
(
=
3.5
6
X
/ n
= 1.429
75 . 75 75 . 5
1 .429
)
= P ( Z 0 . 175 ) = 1 P ( Z 0 . 175 )
= 1 0 .56945 = 0 . 43055
7-9
n = 36
X =
a + b (3 + 1)
=
=2
2
2
X =
(b a + 1)2 1
=
12
X = 2, X =
z=
2/3
=
36
HW 4 FOR STAT601, fall, 2012
1) 7.3, 2) 7.9, 3) 7.10
4) For the insurance of a stereo example from class: Let X=the amount gained by the store by
insuring one customer.
a) What is the expected value of X, []? [derive]
b) What is the distribution of the av
Section 4-2 4-1. a) P (1 < X ) = e - x dx = ( -e - x )
1 2.5
1
= e -1 = 0.3679
2.5 1
b) P (1 < X < 2.5) =
e
1
-x
dx = (-e - x )
= e -1 - e - 2.5 = 0.2858
-x c) P( X = 3) = e dx = 0 3
4
3
-x -x -4 d) P( X < 4) = e dx = (-e ) = 1 - e = 0.9817 0 0
4
e) P(
HW 3 FOR STAT601, fall, 2012
A) Roll a die 10 times, compute the mean number of points, Ill ask you for your outcome in class.
1) 4.1
2) 4.2
3) 4.10
4) 4.15
5) 4.29
6) 4.36
7) 4.41
8) 4.45 a) b) c)
9) 4.46 a) b) d)
10) 4.53
11) 4.113 (and d), derive the c
Section 6-2 6-14. NOTE: The data set contains one additional measurement of 91.2 that should be included in the book. Solutions use this additional measurement. Stem-and-leaf display of octane rating N = 82
Leaf Unit = 0.10 83|4 represents 83.4
1 83|4 3 8
HW 6 FOR STAT601, Fall, 2012
1) 7.29
2) 7.35
For a) Show that the it can be shown expression holds (use a substitution: y = (x2 )/2).
do b) and c) and add
d) Incomes are often assumed to follow a Rayleigh distribution. Here are six annual incomes
in 10s o
Solution of Assignment 6
e x
7-29. f ( x) =
x!
e xi e n
=
L ( ) =
n
xi !
i =1
n
n
xi
i =1
x !
i =1
n
n
i =1
i
i =1
ln L( ) = n ln e + x i ln ln x i !
d ln L ( )
1
= n +
d
n
x
i =1
i
0
n
x
i =1
= n +
n
x
i =1
i
i
=0
= n
n
=
x
i =1
i
n
1 n 2
X i so
n i
HW 7 FOR STAT601, Fall, 2012
1) a) We have seen that the sample standard deviation, s, is a biased estimator of the true standard
deviation, . Using Taylor series estimate the bias and variance of s using information on the bias
and variance of s2 . Assum
HW 9 FOR STAT601, Fall, 2012
1) 5.18 and l) are X and Y independent?
2) 5.25
3) a) Show that for variables X,Y that E(XY )=E(X)E(Y ) if X and Y are independent. Assume
that the domain of X does not depend on that of Y , and conversly. Make the argument fo
Solution to HW7: Problem 1: a) h( x) =
x , so h' ( x) =
1 -3 / 2 1 -1 / 2 and h' ' ( x) = - x x . 4 2
1 1 1 h' ' ( x)( y - x) 2 = h( x) + x -1 / 2 ( y - x) - x -3 / 2 ( y - x) 2 8 2 2
h( y ) h( x) + h' ( x)( y - x) +
Take y = s
2
x = 2 , so 1 1 s + -1 ( s
Solution to HW8:
Problem 1: H 0 : 1 = 2 H a : 1 2
X = X i n and s 2 = ( X i - X ) 2 (n - 1)
i =1 i =1
n
n
Male: n1 = 7, X 1 = 69.57143 and s12 = 7.285714
2 Female: n 2 = 8, X 2 = 64.5 and s 2 = 13.14286 Pooled t-test statistic:
s2 = p
2 (n1 - 1) s12 + (n
STAT 601 Statistical Analysis
Lecture Notes
(2015) Daren B.H. Cline
Department of Statistics
Texas A&M University
Statistics 601 Lecture Notes Table of Contents
Table of Contents
(sections and page numbers are subject to change)
Introduction . 1
A. Objec