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Confidence Interval Mean, σ known, n > 30
A certain medication is known to increase the pulse rate of its users. The
standard deviation of the pulse rate is known to be 5 beats per minute from
previous studies. A sample of 55 users had an average pulse rate of 104
beats per minute. Find the 99% confidence interval of the true mean.
First by calculation:
Since we need the 99% confidence interval we have α = 0.01 and since we
may be in error either high or low we need to split α and find Zα = 2.575 .
2
€
0.005 0.005 Zα = −2.575
Zα = 2.575
2
2
⎛ σ ⎞
⎛ 5 ⎞
Z
=
2.575
Our
error
term
is
E
=
⎜
⎟
⎜
⎟ = 1.736064646 so the
€
€ α 2 ⎝ n ⎠
⎝ 55 ⎠
interval is:
x−E <µ<x+E
102.3 < µ < 105.7
€
⇒€
104 – 1.7 < µ < 104 + 1.7
Now using the calculator to find this interval.
Press Stat
€
←
Select Stats
σ: 5
x :104
n: 55
C-Level:0.99
Calculate
ZInterval (7)
ZInterval
(102.26,105.74)
x :104
n:55
⇒
€
So 102.26 < µ < 105.74