QuestionA simple random sample from a population with a normal distribution of 102 body temperatures has $\bar{x}=98.70^{\circ} \mathrm{F}$ and $\mathrm{s}=0.69^{\circ} \mathrm{F}$. Construct an $80 \%$ confidence interval estimate of the standard deviation of body temperature of all healthy humans.
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Studdy Solution
Convert the variance confidence interval to a standard deviation confidence interval by taking the square root of the endpoints:
$$\left( \sqrt{\frac{101 \times (0.69)^2}{\chi^2_{\text{right}}}}, \sqrt{\frac{101 \times (0.69)^2}{\chi^2_{\text{left}}}} \right)$$
The $80\%$ confidence interval estimate for the standard deviation of body temperature is:
$$\left( \sqrt{\frac{101 \times (0.69)^2}{\chi^2_{\text{right}}}}, \sqrt{\frac{101 \times (0.69)^2}{\chi^2_{\text{left}}}} \right)$$