Question

A simple random sample from a population with a normal distribution of 98 body temperatures has x overbar=98.80degrees Upper F and s=0.67degrees Upper F. Construct a 95​% confidence interval estimate of the standard deviation of body temperature of all healthy humans.

Answer 1

We need to construct the 95% confidence interval for the population variance. We have been provided with the following information about the sample variance and sample size:

s^2 =	0.4489
n=	98

The critical values for α=0.05 and df = 97

degrees of freedom are

and

The corresponding confidence interval is computed as shown below:

Now that we have the limits for the confidence interval, the limits for the 95% confidence interval for the population standard deviation are obtained by simply taking the squared root of the limits of the confidence interval for the variance, so then:

Therefore, based on the data provided, the 95% confidence interval for the population variance is 0.3452<σ2<0.6078,

and the 95% confidence interval for the population standard deviation is 0.5875<σ<0.7796.

please like