Answer: ( 98.04f, 98.40f ), it is not accepted
Step-by-step explanation: the question is suggesting we construct a 99% confidence interval for mean body temperature.
The formulae for Constructing a 99% confidence interval is given below as
u = x + Zα/2 × (s/√n)........... For the upper limit
u = x - Zα/2 × (s/√n)........... For the lower limit
Where u = population mean
x = sample mean = 98.2
s = sample standard deviation = 0.64
n = sample size = 108.
Zα/2 = critical value for a 2 tailed test performed at a 1% level of significance ( 100% - 99%) = 2.58
We are making use of our z test because sample size is greater than 30 ( n = 108).
By substituting the parameters, we have that
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.
Hence the 99% confidence interval for mean temperature of human is ( 98.04f, 98.40f )
Using 98.6f as the average mean body temperature is wrong because it is out of the confidence interval calculated above.
Our confidence interval states that at 99% confidence interval, an average human temperature should be at least 98.04f and at most 98.40f.
98.6f is out of the range.
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