Asimple random sample from a population with a normal distribution of 98 body temperatures has x =98.90 °f and s =0.68°f. construct a 90% 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 1.40°f?

°f

is it safe to conclude that the population standard deviation is less than 1.40°f?

a. this conclusion is not safe because 1.40 °f is in the confidence interval.

b. this conclusion is safe because 1.40 °f is in the confidence interval.

c. this conclusion is not safe because 1.40°f is outside the confidence interval.

d. this conclusion is safe because 1.40 °f is outside the confidence interval.

And the best conclusion would be:

D. This conclusion is safe because 1.40 °F is outside the confidence interval.

Step-by-step explanation:

1) Data given and notation  

s=0.68 represent the sample standard deviation  

represent the sample mean  

n=98 the sample size  

Confidence=90% or 0.90  

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .  

2) Calculating the confidence interval  

The confidence interval for the population variance is given by the following formula:  

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:  

Since the Confidence is 0.90 or 90%, the value of and , and we can use excel, a calculator or a table to find the critical values.  

The excel commands would be: "=CHISQ.INV(0.05,97)" "=CHISQ.INV(0.95,97)". so for this case the critical values are:  

And replacing into the formula for the interval we got:  

Now we just take square root on both sides of the interval and we got:  

And the best conclusion would be:

D. This conclusion is safe because 1.40 °F is outside the confidence interval.

9 x 8 divided by (5-3)=36