10.
83 random samples were selected from a normally distributed population and were found to have a mean of 32.1 and a standard deviation of 2.4. Construct a 90% confidence interval for the population standard deviation.

A.
2.2 < σ < 2.8

B.
28.8 < σ < 37.4

C.
4.6 < σ < 7.8

D.
1.4 < σ < 1.8

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

And the best option would be:

A.  2.2 < σ < 2.8

Step-by-step explanation:

Information provided

represent the sample mean

population mean  

s=2.4 represent the sample standard deviation

n=83 represent the sample size  

Confidence interval

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

The degrees of freedom are given by:

The Confidence is given by 0.90 or 90%, the value of and , the critical values for this case 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 option would be:

A.  2.2 < σ < 2.8

is there a picture

step-by-step explanation: