Confidence Intervals As stated before, researchers often cannot conduct a study on all the individuals in a population (due to funding limitation, time, etc.), so instead they study a sub-sample with the hope of then being able to apply the findings back to the larger population. Since all individuals are not sampled, it means that the "true" mean is never really known. Confidence intervals help to give an indication of how much uncertainty there is in a sample's estimate of the true mean. The more variable the data set, the larger the confidence interval. Small confidence intervals are desirable in studies.
Confidence Intervals As stated before, researchers often cannot conduct a study on all the individuals in a population (due to funding limitation, time, etc.), so instead they study a sub-sample with the hope of then being able to apply the findings back to the larger population. Since all individuals are not sampled, it means that the "true" mean is never really known. Confidence intervals help to give an indication of how much uncertainty there is in a sample's estimate of the true mean. The more variable the data set, the larger the confidence interval. Small confidence intervals are desirable in studies.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Confidence Intervals
As stated before, researchers often cannot conduct a study on all the individuals in a population
(due to funding limitation, time, etc.), so instead they study a sub-sample with the hope of then
being able to apply the findings back to the larger population. Since all individuals are not
sampled, it means that the "true" mean is never really known. Confidence intervals help to give
an indication of how much uncertainty there is in a sample's estimate of the true mean. The
more variable the data set, the larger the confidence interval. Small confidence intervals are
desirable in studies.
In the example we are following, we want to know whether Chocolate B is more effective in
lowering blood pressure than Chocolate A. Comparing the confidence intervals of the two
samples is one way to statically analyze this question. If the confidence intervals do not overlap,
the difference between the groups is statistically significant. If the confidence intervals do
overlap, the statistical difference between the groups is less certain.
Data Set 1 (below) shows the blood pressure readings for each individual in our chocolate study
(10 individuals in the control group, 10 taking chocolate A, and 10 taking chocolate B). The
sample mean and confidence interval are also reported for each group. The confidence interval
reports a low and high blood pressure value around the sample mean (calculated based on the
average, standard deviation, sample size, etc).
Data Set 1
Systolic readings
for control group
Systolic readings
for those taking
Chocolate A
Systolic readings
for those taking
Chocolate B
120
114
99
118
119
118
117
118
114
122
113
120
120
105
115
120
110
use this
data to
create a
data range
Line graph
120
119
119
115
121
118
117
100
120
118
120
120
102
MEAN = Average (mm Hg)
Confidence Interval
first,
120
117
110
(119, 121)
(114.25, 119.75)
(103.5, 116.5)
then
Knowing that non-overlapping intervals indicates that the difference between data sets is
statistically significant, explain your understanding for the ability for chocolate to lower blood
pressure (discuss your comparison of chocolate A and B to one another and to the control group).
Write your answer below:
(USING DATA SET 1)
KEY:
A.
DATA RANGE LINE:
14
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