STATS 500 - Homework 2
Due in class Wednesday, September 28
Based on Chapter 2, problem 1 (page 30)
The dataset teengamb concerns a study of teenage gambling in Britain.
Fit a regression model with the expenditure on gambling as the response and
the sex,
Stat 500
Solutions Homework
1)
a) All registered voters in the state.
b) Simple random sample from a list of registered votes.
2)
The formula can be used, if n 5 and n(1 ) 5 , where satisfies 4 conditions
for binomial experimentsL 1) The experiment consis
STAT500
STAT500 Solutions
1) Problem 11.30
a.
Scatter plot
Scatter Plot of Total Direct Cost vs. Runsize
y (Total cost)
1000
500
0
0
10
20
x (Runsize)
Based on the scatter plot of the data, the data appear to be linear, and the
variance does not appear to
STAT500
Solutions to Homework
1)
a) The data were from an observational study because the investigators did not
control factors in the study environment such as the time spent in exercise (not
set by the investigator). People were merely asked to provide
STAT500
STAT500 Solutions
12.8
b. From Minitab the solution is:
Regression Analysis: protective strength versus dose
The regression equation is
protective strength = 8.67 + 0.575 dose
Predictor
SE Coef
T
P
8.667
1.428
6.07
0.000
0.57527
0.08645
6.65
0.000
STAT 500 - Homework 1
Due in class Wednesday, September 21, 2016
Chapter 1, problem 1 (page 12)
The dataset teengamb concerns a study of teenage gambling in Britain.
Make a numerical and graphical summary of the data, commenting on any
features that you f
STAT 500 - Homework 1
Solutions
Chapter 1, problem 1 (page 12)
We start with a preliminary analysis/summary, and that is shown below. We notice that there
are no missing values. From this summary we see that there were more males sampled than females, 28
Stats 500 Homework 1
Due: October 1
Goals: (1) Learn basic usage of R, including how to load data and generate plots
(2) Practice exploring a dataset
(3) Practice summarizing a dataset, and highlighting interesting features
Note: Because this homework may
Stats 500 HW 2
Due October 6
1. Let x = (x1 , x2 , ., xn ) be a vector of numbers. Dene
n
q
q arg min
|xi |
i=1
Show that
(a) 2 = mean(x)
(b) 1 = median(x)
(Assume that 1 is unique.)
2. For each of the three histograms in Figure 1, answer the following qu
STAT500
Solutions to Homework
1)
Binomial with n = 8 and p = 0.400000
x
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
a)
b)
c)
d)
P( X = x)
0.0168
0.0896
0.2090
0.2787
0.2322
0.1239
0.0413
0.0079
0.0007
x
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
P( X <
STAT500
STAT500 HW Solutions
1)
a) 95% T Confidence Intervals
Variable
speed
10.304)
N
20
Mean
9.100
StDev
2.573
SE Mean
0.575
95.0 % CI
(7.896,
b) The normal probability plot for reading speed suggests no reason to believe that
the data arent normally di
STAT500
STAT500 Solutions
1)
f) False. One cannot prove Ho by just considering type I error.
i) False. P-value less than 0.05 does not guarantee that it is also less than 0.01
2)
The true statements are c, e, g. Others are false.
3)
i.
ii.
iii.
iv.
v.
nor
Chapter 3: Inference
Stats 500, Fall 2016
Brian Thelen, University of Michigan
443 West Hall, bjthelen@umich.edu
1/1
Stats 500 - Chapter 3: Inference
2
Inference
Estimates: 0 , 1 , . . . , p
Draw conclusions about 0 , 1 , . . . , p
Two main inference t
STATS 500 - Homework 3
Due in class Wednesday, October 5, 2016
Problem 2 in Chapter 3 of Faraway (page 49)
Add the following additional problems.
(f ) Derive 95% confidence intervals for the regression coefficients based on
the linear model analysis carri
Statistics 500: Applied Statistics I
Fall of 2016
Class 4:00-5:30 MW in MLB AUD 4
Instructor Information:
Instructor:
Office:
e-mail:
Lectures and Homework:
Office hours:
Brian Thelen
443 West Hall
bjthelen@umich.edu
Posted on Canvas
5:30-6:30 on Monday,
STAT500 Final Review Solutions
STAT500 Final Review Solutions
1) Problem 7.25
a.
S1 = 3.60, S2 = 5.96, where 1 = portfolio1, 2 = portfolio2. So visually it
shows that portfolio2 has a higher risk than portfolio1.
To formally test, we want to conduct the f
STAT500
STAT500 Solutions
1) Problem device
We have independent samples. Furthermore, the two populations (Type I devices
and Type II devices) appear to be normally distributed (see below):
Normal Probability Plot for Type I devic.Type II devi
ML Estimate
STAT500
Solutions to Homework
1) Problem 3.21
a) Mean = 8.04, Median = 1.54.
b) For terrestrial feeder: Mean = 15.01, Median = 6.03; for aquatic feeder: Mean =
0.38, Median = 0.375.
c) The mean is more sensitive to extreme values than is the median. On th
STAT500
Solutions to Homework
1) Problem 4.13
a) A=cfw_6 P(A)= 1/6
b) B=cfw_1,3,5 P(B) = 3/6=1/2
c) C=cfw_4,5,6 P(C) = 3/6=1/2
d) D=cfw_4,6 P(D) = 2/6=1/3
2) Problem 4.20
XY
AB
AC
AD
BC
BD
CD
cfw_Empty
cfw_6
cfw_6
cfw_5
cfw_Empty
cfw_4,6
Mutually exclus
Statistics 500 Applied Statistics
Fall 2015
Instructor:
Johann Gagnon-Bartsch
441 West Hall
johann.teaching@gmail.com (do NOT use johanngb@umich.edu)
Office hours: Tu 10:00-11:00 and Tu 1:00-1:30, or by appointment
GSI:
Yura Kim
kimyr@umich.edu
Office hou