Introduction to Statistics (with calculus)
Statistics W1211 Fall 2014
Section 002: MW 6:10pm7:25pm; 517 Hamilton
Instructor:
Ronald Neath
[email protected]
Oce hours:
Time and location to be announced
Course description: This is a rst course in statist
Statistics W1211 Fall 2014
Midterm Exam 1
Answers
1. (5 points) The following density histogram summarizes the distribution of average length of
stay (in days) for a random sample of U.S. hospitals.
0.15
0.10
0.00
0.05
Density
0.20
0.25
Histogram of avera
Statistics W1211 Fall 2014
Midterm Exam 2
Answers
1. In a survey of n = 1000 American adults, 248 said the believed in astrology. Calculate and
interpret a 99% condence interval for the proportion of all adult Americans who believe in
astrology.
p z/2
p(1
Introduction to Statistics (with calculus)
Statistics W1211 Fall 2014
Assignment 4
Solutions:
1. Chapter 4 problem 34
Let X denote the substrate concentration (mg/cm3 ) for a random sample of reactor
inuent so
X N ( = .30, 2 = .062 )
(a)
P (X > .25) = P
X
Introduction to Statistics (with calculus)
Statistics W1211 Fall 2014
Assignment 5
Solutions:
1. Chapter 5 problem 42
(a) We must compute x for each of the
6
2
= 15 possible samples.
Sample
x
probability
1,2
31.65
1/15
1,3
29.95
1/15
1,4
31.65
1/15
1,5
27
Introduction to Statistics (with calculus)
Statistics W1211 Fall 2014
Assignment 9
Solutions:
1. Chapter 2 problem 56
P (A|B) + P (A |B) =
P (B)
P (A B) P (A B)
+
=
=1
P (B)
P (B)
P (B)
2. Chapter 2 problem 58
P (A C) (B C)
P (A B) C)
=
P (C)
P (C)
P (A C
Introduction to Statistics (with calculus)
Statistics W1211 Fall 2014
Assignment 8
Solutions:
1. Chapter 8 problem 54
If the taster is merely guessing, he or she has a 1/3 chance of correctly identifying the
bottle that is dierent from the other two. Lett
Introduction to correlation and regression
Statistics W1211
Columbia University
Fall 2014
December 8, 2014
1
Bivariate data
A bivariate data set consists of two measurements on each subject.
Data: (x1, y1), (x2, y2), . . . , (xn, yn)
Example:
xi = height
Introduction to Statistics (with calculus)
Statistics W1211 Fall 2014
Assignment 6
Solutions:
1. Chapter 7 problem 12.
In a random sample of size n = 110 we observe sample mean x = 0.81 and standard
deviation s = 0.34. We want a 99% condence interval for
Introduction to Statistics (with calculus)
Statistics W1211 Fall 2014
Assignment 1
Solutions:
1. Chapter 1 problem 26.
(a) The proportion smaller than 15 is .177 + .166 + .175 = .518 so the assertion
is true.
(b) The proportion that are at least 30 is .07
Introduction to Statistics (with calculus)
Statistics W1211 Fall 2014
Assignment 2
Solutions:
1. Chapter 2 problem 12.
(a) P (A B) = P (A) + P (B) P (A B) = .50 + .40 .25 = .65
(b) P (A B ) = 1 P (A B) = 1 .65 = .35
(c) P (A B ) = P (A) P (A B) = .50 .25
Introduction to Statistics (with calculus)
Statistics W1211 Fall 2014
Assignment 7
Solutions:
1. Chapter 8 problem 18.
We have a Normal population with unknown and = 9. We will test the hypotheses
H0 : = 75
versus
Ha : < 75
based on a random sample of n =
STAT UN1202 HW1 Solution
2.6. A college library has five copies of a certain text on reserve. Two copies (1 and 2) are first
printings, and the other three (3, 4, and 5) are second printings. A student examines these
books in random order, stopping onl
UN1201 HW10 Solution
13.12. a. Could a linear regression result in residuals 23, -27, 5, 17, -8, 9, and 15? Why or why
not?
b. Could a linear regression result in residuals 23, -27, 5, 17, -8, -12, and 2 corresponding to x
values 3, -4, 8, 12, -14, -2
STAT W1211 INTRODUCTION TO STATISTICS SEC 003
Spring 2012
Instructor
Xuan Yang
Oce:
Email:
Oce Hours:
901 SSW, 1255 Amsterdam Ave
[email protected]
4:00-5:00 pm, Thursday
Class Time
1:10 - 2:25 pm, Monday, 903 SSW. 1:10 - 2:25 pm, Wednesday, 703 Ham.
De
UN 1201 HW07 Solutions
8.2
a. Comply.
b. Do not comply. The alternative hypothesis should not include equality.
c. Do not comply. The null hypothesis should not include inequality while the alternative
should not
UN 1201 HW3 Solutions
3.52
a. Let X be the number who want a new copy of the book. X follows a binomial
distribution Bin(25,.3)(n=25, p=.3).
So the mean value is:
= = 25 .3 = 7.5
The standard devi
UN 1201 HW4 solution
4.20. Consider the pdf for total waiting time Y for two buses
1
,
0<5
25
= 2 1
,
5 10
5 25
0,
a. Compute and sketch the cdf of Y. [Hint: Consider separately 0 < 5 and 5 10 in
computing F(y). A graph of the pdf should be helpf
UN1201 HW8 Solution
9.4. Reliance on solid biomass fuel for cooking and heating exposes many children from
developing countries to high levels of indoor air pollution. The article Domestic Fuels, Indoor
Air Pollution, and Childrens Health (Annals of th
UN1201 HW6
6.8. In a random sample of 80 components of a certain type, 12 are found to be defective.
a. Give a point estimate of the proportion of all such components that are not defective.
b. A system is to be constructed by randomly selecting two of
UN1201 HW2 Solution
3.10. The number of pumps in use at both a six-pump station and a four-pump
station will be determined. Give the possible values for each of the following
random variables:
a. T = the total number of pumps in use
b. X = the differ