Question

A simple random sample from a population with a normal distribution of 108 body temperatures has x=98.20 F and s=0.67 F. Construct a 99% confidence interval estimate of the standard deviation of body temperature of all healthy humans. Is it safe to conclude that the population standard deviation is less than 0.90°F? Click the icon to view the table of Chi-Square critical values (Round to two decimal places as needed.) Is it safe to conclude that the population standard deviation is less than 0.90°F?

A. This conclusion is not safe because 0.90°F is outside the confidence interval.
B. This conclusion is not safe because 0.90 F is in the confidence interval.
C. This conclusion is safe because 0.90° F is outside the confidence interval.
D. This conclusion is safe because 0.90° F is in the confidence interval

Answer 1

To construct a 99% confidence interval estimate of the standard deviation of body temperature, use the formula and plug in the given values. Since 0.90°F is outside the confidence interval, it is not safe to conclude that the population standard deviation is less than 0.90°F.

Step-by-step explanation:

To construct a 99% confidence interval estimate of the standard deviation of body temperature, we can use the formula:

Lower Limit: Degrees of freedom * s2 / X2 * χ2 (α/2,n-1)

Upper Limit: Degrees of freedom * s2 / X2 * χ2 (1-α/2,n-1)

Plugging in the given values, we have:

Lower Limit: 19 * 0.672 / 108 * X2 (0.01/2, 107)

Upper Limit: 19 * 0.672 / 108 * X2 (1- 0.01/2, 107)

which gives us a confidence interval of [0.5549, 1.0588]

Since 0.90°F is outside the confidence interval, it is not safe to conclude that the population standard deviation is less than 0.90°F.