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
Introduction to Statistics (with calculus)
Statistics W1211 Fall 2014
Section 002: MW 6:10pm7:25pm; 517 Hamilton
Instructor:
Ronald Neath
rcn2112@columbia.edu
Oce hours:
Time and location to be announced
Course description: This is a rst course in statist
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 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 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 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 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 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 =
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 Spring 2016
Section 002: TR 11:40am12:55pm; 309 Havemeyer
Instructor:
Ronald Neath
rcn2112@columbia.edu
Office hours:
Time and location to be announced
Course description: This is a first course