STA 032 Sample Exam II
True/False
For each of the following questions indicate true or false, then explain your answer. You may use examples
to illustrate your answer.
only if n 30 we know
(I) For a general population X, and the corresponding sample aver
STA 032 Spring 2016
Homework 1 - Due Friday, April 18th
Reminder: Book homework and R homework are to be
turned in to separate piles
(a) Find the median of this dataset.
(b) Find the first, third, and second quartiles.
(c) Find the 10th and 90th percentil
STA 32 - Spring 2015 - R Homework 1 - Due Friday, April 10th
An introduction statistics course from a Washington university was polled, and their gender, and their
college GPA, their number of siblings, and their highschool GPA was recorded in LargeIntro.
STA 032 Winter 2016
Homework 7 - Due Friday, March 11th Reminder: Book
homework and R homework are to be turned in to separate
piles
(a) Identify the dependent/response variable, and the independent/explanatory variable.
(b) State the null and alternative
STA 032 Winter 2016 Homework 7 Solutions
Erin K. Melcon
Book Homework
1. (a) Let X = smoker group, Y =non-smoker. The null hypothesis is: H0 : X Y , with alternative HA : X > Y .
y )0
(9088)0
(b) The test-statistic is ts = q(x
=p
=
2
2
5.22
6.32
s
X
nX
s
STA 032 Spring 2015
Homework 3 - Solutions
1. (a) The c.d.f can be found below:
X
F (x)
1
0.60
2
0.80
3
0.95
4
0.98
5
1
(b) At least one commuter means
P (X 1) = 1 P (X < 1) = 1 P (X = 0) = 1 0 = 1.
(c) Between 2 and 4 inclusive means
P (2 X 4) = P (X = 2
STA 32 Homework 2 Solutions
Section 2.2
Problem 4
10
5
=
10!
= 252
5!5!
Problem 7
(210 )(45 ) = 1048576
Problem 12
P (match) = P (RR) + P (GG) + P (BB)
= (6/12)(5/11) + (4/12)(3/11) + (2/12)(1/11)
= 1/3
Section 2.3
Problem 2
A and B are independent if P (
STA 032 Spring 2015
Homework 7 - Solutions
1. Notice that since the sample size is large, we can use Z/2 . Let population 1 be third party consultants, population 2
be in-house training.
2
2
s
s
482
(a) (X Y ) Z/2 nX + nY (500 490) 1.96 180 +
X
Y
So tha
5/9/14
"Dont eat the data !
Small-Sample C.|. for two means
If the samples are small, then we must use the f-olfstrlldioq
However, we now have two variances 0/; M 037
Act-{l CUB al'lha+;A
The C.l.is constructed based on assuming 0K :93! 0,. of :f 0;
u
5/5/14
"Be careful about reading health books. You may die of a misprint. - Mark Twain
Example 4.71 from page 293
At a large university, the mean age of the students is 22.3 years, and the standard deviation is
4 years. A random sample of 64 students i
1
5/2/14
"To understand Gods thoughts, we must study statistics, for these are the measure of his
purpose. -Florence Nightingale
2014 04 30 Poisson Distribution.R
2014 04 30 Normal Distribution.R
Linear Combinations of Normal R.V.
F XIV/V0959 1,
L21,
5/7/14
"Nobody goes there anymore; it's too crowded." - Yogi Berra
5.3 Small-Sample CI. for Population Mean M.
When n is small 430 , the data must be from a norm! oils-érhguéim
Because rm/(MR), then 7 is normal.
X MU (14 (a A x
However, when we estima
1
4/2/14
"The non-scientist in the street probably has a clearer notion of physics, chemistry and biology
than of statistics, regarding statisticians as numerical philatelists, mere collector of numbers.
Stephen Senn, Dicing with Death: Chance, Risk a
dat = read.table("Midterm1Salaries.txt", header = T)
attach(dat)
#
#large sample c.i.
x.bar = mean(women)
s.d = sd(women)
n = length(women)
#confidence level is 1-alpha
alpha = 0.05
#to find the critical value
#in R, the function qnorm gives you the area
1
4/30/14
"If people do not believe that mathematics is simple, it is only because they do not realize how
complicated life is. -John Louis von Neumann
4.3 The Poisson Distribution .
if the random variable x is the number of events occurring in 3 gm! Ak
1
4/28/14
"Statistical thinking will one day be as necessary for efficient citizenship as the ability to read
and write." -H.G. Wells
4.1 The Bernoulli Distribution
Experiments that result in one of two outrun)" is called a
fer/ion; trial
One outcome
5/30/14
"A line is a clot that went for a walk. - Paul Klee
6.11 The F Test for Eguality of Variance
Let X... {XM
be a random sample from a NCM or?)
I
We know that the sample mean
Y N/l/(M, £1)
P
What is the distribution of 5,} .
This is not easy
STA 032 Spring 2015
Homework 4, due May 6th
1. Suppose that the probability of getting an A in a particular course is 0.08, and assume that the all student grades
are independent. If you randomly sample 20 students
taking the course;
(a) Find the expected
STA 32 - Winter 2015 - R Homework 3 - Due Friday, February 13th
Problem 1
The goal of this problem is to create your own function which calculates binomial probabilities. Your function can be called whatever you want, and should take in arguments x, n, p,
STA 32 - Winter 2015 - R Homework 5 - Due Friday, March 6th
Problem 1
The goal of this simulation problem is to examine how accurate the normal approximation
to binomial is without the continuity correction.
Create a function that takes in x (the number o
5/12/14
"The hardest arithmetic to master is that which enables us to count our blessings.
-Eric Hoffer
5.7 CI. with Paired Data
The CI. we discussed so far, assumed
X owl 7 an Indefmdui-
Wenowdiscussa CI. For View
+kc1 °Ue defuaiad'.
For these inter
5/14/14
"The most important questions of life are, for the most part, really only problems of
probability." Pierre Simon, Marquis de Laplace
Examples of C.|.sI P.l.s, and T.l.'s
@Suppose a student measuring the boiling temperature of a certain liquid o
1
5/16/14
"Mini cupcakes? As in the mini version of regular cupcakes? Which is already a mini version of
cake? Honestly, where does it end with you people?" - Kevin Malone
Hypothesis Testing
in inferential statistics, we are interested in an unknown (Du
STA 032 Spring 2015
Homework 4, due May 13th
1. Assume weights of cats of a certain breed are normally
distributed with mean 4.1kg and standard deviation
0.6kg. Assume all cats weights are independent.
5. In a particular state, a major ood happens once ev
1
5/19/14
"The problem with internet quotes is that you cant always depend on their accuracy"
-Abraham Lincoln, 1864
Hypothesis test examples:
The article "Wear in Boundary Lubrication (S. Hsu, R. Munro, and M. Shen, Journal of Engineering Tribology,
2
1
4/2/14
Two things are infinite, the universe and human stupidity, and I am not yet completely
sure about the universe. -Albert Einstein
Summary Statistics
Notation for arbitrary data set:
The sample mean:
Measure of Variability:
The spread of the data c
Poisson Random Variables (Rees: 6.86.14)
Examples: What is the distribution of:
the number of organisms in the squares of a haemocytometer?
the number of hits on a web site in one hour?
the number of goals scored by a football team in a match?
the num
STA 032 Week 6 R handout
1. Some useful functions
Here are some functions that may be useful in the future:
sqrt(x): calculates the square root of a single integer, or of each element of a vector.
sqrt(100)
# [1] 10
sqrt(c(4,16,81,121)
# [1]
2
4
9 11
fa
STA 032 Spring 2017
Homework 3 - Due Monday, May 15th
Reminder: Book homework is submitted in lecture and R
homework is submitted on Canvas.
4. Suppose that the number of cars arriving at a given intersection has an average rate of 3 per second. Assume
ca