Question

A simple random sample from a population with a normal distribution of 102 body temperatures has x overbarequals98.40degrees Upper F and sequals0.66degrees Upper F. Construct an 80​% 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 1.80degrees Upper F​?

Answer 1

Answer:

It is 80% statistically safe to conclude that the population standard deviation is less than 1.8°F

Step-by-step explanation:

The given information are;

The sample size, n = 102

The sample mean = 98.4°F

The sample standard deviation = 0.66°F

$\sqrt{\dfrac{\left (n-1 \right )s^{2}}{\chi _{\alpha /2}^{}}}< \sigma < \sqrt{\dfrac{\left (n-1 \right )s^{2}}{\chi _{1-\alpha /2}^{}}}$

α = 0.2, ∴ α/2 = 0.1

$\chi _{1-\alpha /2}$ = $\chi _{0.9, 101}$ = 83.267

$\chi _{\alpha /2}$ = $\chi _{0.1, 101}$ = 119.589,

Which gives;

$\sqrt{\dfrac{\left (102-1 \right )0.66^{2}}{119.589}^{}}}< \sigma < \sqrt{\dfrac{\left (102-1 \right )0.66^{2}}{83.267}^{}}}$

0.607 < σ <0.727

Therefore, it is 80% statistically safe to conclude that the population standard deviation is less than 1.8°F.