Sample Size Formula (Part 1) From Formula 7.2, an estimate for margin of error for a 95 % confidence interval is m = 2 p ^ 1 − p ^ n where n is the required sample size and p ^ is the sample proportion. Since we do not know a value for p ^ , we use a conservative estimate of 0.50 for p ^ . Replace p ^ with 0.50 in the formula and simplify.
Sample Size Formula (Part 1) From Formula 7.2, an estimate for margin of error for a 95 % confidence interval is m = 2 p ^ 1 − p ^ n where n is the required sample size and p ^ is the sample proportion. Since we do not know a value for p ^ , we use a conservative estimate of 0.50 for p ^ . Replace p ^ with 0.50 in the formula and simplify.
Solution Summary: The author explains how to simplify the given formula by replacing stackrelp with 0.50.
Sample Size Formula (Part 1) From Formula 7.2, an estimate for margin of error for a
95
%
confidence interval is
m
=
2
p
^
1
−
p
^
n
where
n
is the required sample size and
p
^
is the sample proportion. Since we do not know a value for
p
^
, we use a conservative estimate of
0.50
for
p
^
. Replace
p
^
with
0.50
in the formula and simplify.
Definition Definition Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.
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Part (b)
Draw a scatter plot of the ordered pairs.
N
Life
Expectancy
Life
Expectancy
80
70
600
50
40
30
20
10
Year of
1950
1970 1990
2010 Birth
O
Life
Expectancy
Part (c)
800
70
60
50
40
30
20
10
1950
1970 1990
W
ALT
林
$
#
4
R
J7
Year of
2010 Birth
F6
4+
80
70
60
50
40
30
20
10
Year of
1950 1970 1990
2010 Birth
Life
Expectancy
Ox
800
70
60
50
40
30
20
10
Year of
1950 1970 1990 2010 Birth
hp
P.B.
KA
&
7
80
% 5
H
A
B
F10
711
N
M
K
744
PRT SC
ALT
CTRL
Harvard University
California Institute of Technology
Massachusetts Institute of Technology
Stanford University
Princeton University
University of Cambridge
University of Oxford
University of California, Berkeley
Imperial College London
Yale University
University of California, Los Angeles
University of Chicago
Johns Hopkins University
Cornell University
ETH Zurich
University of Michigan
University of Toronto
Columbia University
University of Pennsylvania
Carnegie Mellon University
University of Hong Kong
University College London
University of Washington
Duke University
Northwestern University
University of Tokyo
Georgia Institute of Technology
Pohang University of Science and Technology
University of California, Santa Barbara
University of British Columbia
University of North Carolina at Chapel Hill
University of California, San Diego
University of Illinois at Urbana-Champaign
National University of Singapore
McGill…
Name
Harvard University
California Institute of Technology
Massachusetts Institute of Technology
Stanford University
Princeton University
University of Cambridge
University of Oxford
University of California, Berkeley
Imperial College London
Yale University
University of California, Los Angeles
University of Chicago
Johns Hopkins University
Cornell University
ETH Zurich
University of Michigan
University of Toronto
Columbia University
University of Pennsylvania
Carnegie Mellon University
University of Hong Kong
University College London
University of Washington
Duke University
Northwestern University
University of Tokyo
Georgia Institute of Technology
Pohang University of Science and Technology
University of California, Santa Barbara
University of British Columbia
University of North Carolina at Chapel Hill
University of California, San Diego
University of Illinois at Urbana-Champaign
National University of Singapore…
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