High School

A data set includes 103 body temperatures of healthy adult humans, with a mean of 98.1 degrees F and a standard deviation of 0.56 degrees F.

Construct a 99% confidence interval estimate of the mean body temperature of all healthy humans.

What does the sample suggest about the use of 98.6 degrees F as the mean body temperature?

Answer :

Answer:

The 99% confidence interval estimate for the mean is 97.9576 ≤ μ ≤ 98.246

A) This suggests that the mean body temperature could very possibly be 98.6 °F

Step-by-step explanation:

The number of body temperatures, n = 103

The mean body temperature, [tex]\bar x[/tex] = 98.1

The standard deviation, s = 0.56

Confidence interval required = 99%

Confidence interval, CI is given by

[tex]CI=\bar{x}\pm z\frac{s}{\sqrt{n}}[/tex]

Plugging in the values we get;

z = 2.56 at 99%

[tex]CI=98.1}\pm 2.56\times \frac{0.56}{\sqrt{103}}[/tex]

Therefore, we have

[tex]\mu_{min} = 97.9579 , \ \mu_{max} = 98.242[/tex],

The statistical result suggest that at 99% confidence level, the sample mean temperature is likely to be 98.1 °F

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