Answer :
The 99% confidence interval for mean temperature of human is :
( 98.04f, 98.40f )
A data set includes 108 body temperatures of healthy adult humans having a mean of 98.2 and a standard deviation of 0.64 .
Now, We have to construct a 99% confidence interval estimate of the mean body temperature of all healthy humans.
We use these formula for upper limit and lower limit:
u = x + Zα/2 × (s/√n) (For the upper limit)
u = x - Zα/2 × (s/√n) (For the lower limit)
We have the information from question:
x = sample mean = 98.2
s = standard deviation = 0.64
n = sample size = 108.
[tex]Z_\frac{\alpha }{2}[/tex] = critical value for a 2 tailed test performed at a 1% level of significance ( 100% - 99%) = 2.58
Now, Substitute the parameter,
For upper limit:
u = x + Zα/2 × (s/√n)
u = 98.2 + 2.58 ( 0.64/√108)
u = 98.2 + 2.58 ( 0.0616)
u = 98.2 + 0.1589
u = 98.4
For lower limit:
u = x - Zα/2 × (s/√n)
u = 98.2 - 2.58 ( 0.64/√108)
u = 98.2 - 2.58 ( 0.0616)
u = 98.2 - 0.1589
u = 98.04.
The 99% confidence interval for mean temperature of human is :
( 98.04f, 98.40f )
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