A data set includes 103 body temperatures of healthy adult humans for which x ov
ID: 3179772 • Letter: A
Question
A data set includes
103
body temperatures of healthy adult humans for which
x overbar
equals98.1degrees
F
and
s equals 0.56 degrees Upper F
.
Complete parts (a) and (b) below.Click here to view a t distribution table.
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Click here to view page 1 of the standard normal distribution table.
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Click here to view page 2 of the standard normal distribution table.
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a. What is the best point estimate of the mean body temperature of all healthy humans?
The best point estimate is
98.1
degrees
F.
(Type an integer or a decimal.)
b. Using the sample statistics, construct a
99
%
confidence interval estimate of the mean body temperature of all healthy humans. Do the confidence interval limits contain
98.6degrees
F?
What does the sample suggest about the use of
98.6degrees
F
as the mean body temperature?
What is the confidence interval estimate of the population mean
mu
?
nothing
degreesFless thanmuless thannothingdegrees
F
(Round to three decimal places as needed.)
Explanation / Answer
Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=98.1
Standard deviation( sd )=0.56
Sample Size(n)=103
Confidence Interval = [ 98.1 ± t a/2 ( 0.56/ Sqrt ( 103) ) ]
= [ 98.1 - 2.625 * (0.055) , 98.1 + 2.625 * (0.055) ]
= [ 97.955,98.245 ]
a. What is the best point estimate of the mean body temperature of all healthy humans
point estimate = 98.1
b.
[ 97.955,98.245 ]
c.
Interpretations:
1) We are 99% sure that the interval [97.955 , 98.245 ] contains the true population mean
2) If a large number of samples are collected, and a confidence interval is created
for each sample, 99% of these intervals will contains the true population mean
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